diff --git a/.coveragerc b/.coveragerc
index 3ca2751a9..9dfac6599 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -1,5 +1,5 @@
 [report]
-fail_under = 90
+fail_under = 91
 
 [run]
 source = pystac
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1e423a8b7..86bb0ed87 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,8 @@
   STAC Items ([#430](https://github.com/stac-utils/pystac/pull/430))
 - Support for Python 3.9 ([#420](https://github.com/stac-utils/pystac/pull/420))
 - Migration for pre-1.0.0-rc.1 Stats Objects (renamed to Range Objects in 1.0.0-rc.3) ([#447](https://github.com/stac-utils/pystac/pull/447))
+- Attempting to extend a `STACObject` that does not contain the extension's schema URI in
+  `stac_extensions` raises new `ExtensionNotImplementedError` ([#450](https://github.com/stac-utils/pystac/pull/450))
 
 ### Changed
 
@@ -20,6 +22,9 @@
   `StacIO.read_text` ([#433](https://github.com/stac-utils/pystac/pull/433))
 - `FileExtension` updated to work with File Info Extension v2.0.0 ([#442](https://github.com/stac-utils/pystac/pull/442))
 - `FileExtension` only operates on `pystac.Asset` instances ([#442](https://github.com/stac-utils/pystac/pull/442))
+- `*Extension.ext` methods now have an optional `add_if_missing` argument, which will
+  add the extension schema URI to the object's `stac_extensions` list if it is not
+  present ([#450](https://github.com/stac-utils/pystac/pull/450))
 
 ### Fixed
 
@@ -377,4 +382,3 @@ Initial release.
 [v0.3.2]: <https://github.com/stac-utils/pystac/compare/v0.3.1..v0.3.2>
 [v0.3.1]: <https://github.com/stac-utils/pystac/compare/v0.3.0..v0.3.1>
 [v0.3.0]: <https://github.com/stac-utils/pystac/tree/v0.3.0>
-
diff --git a/docs/api.rst b/docs/api.rst
index 08ef5fe11..91469842b 100644
--- a/docs/api.rst
+++ b/docs/api.rst
@@ -414,6 +414,43 @@ AssetProjectionExtension
    :members:
    :show-inheritance:
 
+Raster Extension
+----------------
+
+DataType
+~~~~~~~~
+
+.. autoclass:: pystac.extensions.raster.DataType
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Statistics
+~~~~~~~~~~
+
+.. autoclass:: pystac.extensions.raster.Statistics
+   :members:
+
+Histogram
+~~~~~~~~~
+
+.. autoclass:: pystac.extensions.raster.Histogram
+   :members:
+
+RasterBand
+~~~~~~~~~~
+
+.. autoclass:: pystac.extensions.raster.RasterBand
+   :members:
+
+RasterExtension
+~~~~~~~~~~~~~~~
+
+.. autoclass:: pystac.extensions.raster.RasterExtension
+   :members:
+   :show-inheritance:
+   :inherited-members:
+
 Scientific Extension
 --------------------
 
diff --git a/docs/contributing.rst b/docs/contributing.rst
index 66335b810..aa1cba281 100644
--- a/docs/contributing.rst
+++ b/docs/contributing.rst
@@ -62,7 +62,7 @@ example, to format all the Python code, run ``pre-commit run --all-files black``
 
 You can also install a Git pre-commit hook which will run the relevant linters and
 formatters on any staged code when committing. This will be much faster than running on
-all files, which is usually[#]_ only required when changing the pre-commit version or
+all files, which is usually [#]_ only required when changing the pre-commit version or
 configuration. Once installed you can bypass this check by adding the ``--no-verify``
 flag to Git commit commands, as in ``git commit --no-verify``.
 
diff --git a/pystac/__init__.py b/pystac/__init__.py
index 19732af9b..749fcfb63 100644
--- a/pystac/__init__.py
+++ b/pystac/__init__.py
@@ -7,6 +7,7 @@
     STACError,
     STACTypeError,
     ExtensionAlreadyExistsError,
+    ExtensionNotImplemented,
     ExtensionTypeError,
     RequiredPropertyMissing,
     STACValidationError,
diff --git a/pystac/errors.py b/pystac/errors.py
index 488ae781b..a5eae5df4 100644
--- a/pystac/errors.py
+++ b/pystac/errors.py
@@ -35,6 +35,11 @@ class ExtensionAlreadyExistsError(Exception):
     pass
 
 
+class ExtensionNotImplemented(Exception):
+    """Attempted to extend a STAC object that does not implement the given
+    extension."""
+
+
 class RequiredPropertyMissing(Exception):
     """This error is raised when a required value was expected
     to be there but was missing or None. This will happen, for example,
diff --git a/pystac/extensions/base.py b/pystac/extensions/base.py
index 8f496dcf0..d33707ffa 100644
--- a/pystac/extensions/base.py
+++ b/pystac/extensions/base.py
@@ -1,7 +1,7 @@
 from abc import ABC, abstractmethod
 from typing import Generic, Iterable, List, Optional, Dict, Any, Type, TypeVar, Union
 
-from pystac import Collection, RangeSummary, STACObject, Summaries
+import pystac
 
 
 class SummariesExtension:
@@ -12,16 +12,16 @@ class SummariesExtension:
     extension-specific class that inherits from this class and instantiate that. See
     :class:`~pystac.extensions.eo.SummariesEOExtension` for an example."""
 
-    summaries: Summaries
+    summaries: pystac.Summaries
     """The summaries for the :class:`~pystac.Collection` being extended."""
 
-    def __init__(self, collection: Collection) -> None:
+    def __init__(self, collection: pystac.Collection) -> None:
         self.summaries = collection.summaries
 
     def _set_summary(
         self,
         prop_key: str,
-        v: Optional[Union[List[Any], RangeSummary[Any], Dict[str, Any]]],
+        v: Optional[Union[List[Any], pystac.RangeSummary[Any], Dict[str, Any]]],
     ) -> None:
         if v is None:
             self.summaries.remove(prop_key)
@@ -77,7 +77,7 @@ def _set_property(
             self.properties[prop_name] = v
 
 
-S = TypeVar("S", bound=STACObject)
+S = TypeVar("S", bound=pystac.STACObject)
 
 
 class ExtensionManagementMixin(Generic[S], ABC):
@@ -124,3 +124,17 @@ def has_extension(cls, obj: S) -> bool:
             obj.stac_extensions is not None
             and cls.get_schema_uri() in obj.stac_extensions
         )
+
+    @classmethod
+    def validate_has_extension(cls, obj: Union[S, pystac.Asset]) -> None:
+        """Given a :class:`~pystac.STACObject` or :class:`pystac.Asset` instance, checks
+        if the object (or its owner in the case of an Asset) has this extension's schema
+        URI in it's :attr:`~pystac.STACObject.stac_extensions` list."""
+        extensible = obj.owner if isinstance(obj, pystac.Asset) else obj
+        if (
+            extensible is not None
+            and cls.get_schema_uri() not in extensible.stac_extensions
+        ):
+            raise pystac.ExtensionNotImplemented(
+                f"Could not find extension schema URI {cls.get_schema_uri()} in object."
+            )
diff --git a/pystac/extensions/datacube.py b/pystac/extensions/datacube.py
index 414400cf9..e43b8de4c 100644
--- a/pystac/extensions/datacube.py
+++ b/pystac/extensions/datacube.py
@@ -337,13 +337,22 @@ def dimensions(self, v: Dict[str, Dimension]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "DatacubeExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "DatacubeExtension[T]":
         if isinstance(obj, pystac.Collection):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(DatacubeExtension[T], CollectionDatacubeExtension(obj))
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(DatacubeExtension[T], ItemDatacubeExtension(obj))
         elif isinstance(obj, pystac.Asset):
+            if add_if_missing and obj.owner is not None:
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
             return cast(DatacubeExtension[T], AssetDatacubeExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
diff --git a/pystac/extensions/eo.py b/pystac/extensions/eo.py
index d266296b1..576d1c6ba 100644
--- a/pystac/extensions/eo.py
+++ b/pystac/extensions/eo.py
@@ -346,8 +346,8 @@ def cloud_cover(self, v: Optional[float]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "EOExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "EOExtension[T]":
         """Extends the given STAC Object with properties from the :stac-ext:`Electro-Optical
         Extension <eo>`.
 
@@ -359,8 +359,14 @@ def ext(obj: T) -> "EOExtension[T]":
             pystac.ExtensionTypeError : If an invalid object type is passed.
         """
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(EOExtension[T], ItemEOExtension(obj))
         elif isinstance(obj, pystac.Asset):
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
             return cast(EOExtension[T], AssetEOExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
diff --git a/pystac/extensions/file.py b/pystac/extensions/file.py
index ebee4f475..deb1df4b0 100644
--- a/pystac/extensions/file.py
+++ b/pystac/extensions/file.py
@@ -193,13 +193,21 @@ def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
     @classmethod
-    def ext(cls, obj: pystac.Asset) -> "FileExtension":
+    def ext(cls, obj: pystac.Asset, add_if_missing: bool = False) -> "FileExtension":
         """Extends the given STAC Object with properties from the :stac-ext:`File Info
         Extension <file>`.
 
         This extension can be applied to instances of :class:`~pystac.Asset`.
         """
-        return cls(obj)
+        if isinstance(obj, pystac.Asset):
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
+            return cls(obj)
+        else:
+            raise pystac.ExtensionTypeError(
+                f"File Info extension does not apply to type {type(obj)}"
+            )
 
 
 class FileExtensionHooks(ExtensionHooks):
diff --git a/pystac/extensions/item_assets.py b/pystac/extensions/item_assets.py
index 5b362017d..f85451c0f 100644
--- a/pystac/extensions/item_assets.py
+++ b/pystac/extensions/item_assets.py
@@ -117,8 +117,17 @@ def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
     @classmethod
-    def ext(cls, collection: pystac.Collection) -> "ItemAssetsExtension":
-        return cls(collection)
+    def ext(
+        cls, obj: pystac.Collection, add_if_missing: bool = False
+    ) -> "ItemAssetsExtension":
+        if isinstance(obj, pystac.Collection):
+            if add_if_missing:
+                cls.add_to(obj)
+            return cls(obj)
+        else:
+            raise pystac.ExtensionTypeError(
+                f"Item Assets extension does not apply to type {type(obj)}"
+            )
 
 
 class ItemAssetsExtensionHooks(ExtensionHooks):
diff --git a/pystac/extensions/label.py b/pystac/extensions/label.py
index 9e3f98431..745d991d7 100644
--- a/pystac/extensions/label.py
+++ b/pystac/extensions/label.py
@@ -639,13 +639,21 @@ def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
     @classmethod
-    def ext(cls, obj: pystac.Item) -> "LabelExtension":
+    def ext(cls, obj: pystac.Item, add_if_missing: bool = False) -> "LabelExtension":
         """Extends the given STAC Object with properties from the :stac-ext:`Label
         Extension <label>`.
 
         This extension can be applied to instances of :class:`~pystac.Item`.
         """
-        return cls(obj)
+        if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
+            return cls(obj)
+        else:
+            raise pystac.ExtensionTypeError(
+                f"Label extension does not apply to type {type(obj)}"
+            )
 
 
 class LabelExtensionHooks(ExtensionHooks):
diff --git a/pystac/extensions/pointcloud.py b/pystac/extensions/pointcloud.py
index c3cf863a4..804fed2c2 100644
--- a/pystac/extensions/pointcloud.py
+++ b/pystac/extensions/pointcloud.py
@@ -522,15 +522,21 @@ def statistics(self, v: Optional[List[PointcloudStatistic]]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "PointcloudExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "PointcloudExtension[T]":
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(PointcloudExtension[T], ItemPointcloudExtension(obj))
         elif isinstance(obj, pystac.Asset):
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
             return cast(PointcloudExtension[T], AssetPointcloudExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
-                f"File extension does not apply to type {type(obj)}"
+                f"Pointcloud extension does not apply to type {type(obj)}"
             )
 
 
diff --git a/pystac/extensions/projection.py b/pystac/extensions/projection.py
index efa121b06..1c68c9fa0 100644
--- a/pystac/extensions/projection.py
+++ b/pystac/extensions/projection.py
@@ -237,8 +237,8 @@ def transform(self, v: Optional[List[float]]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "ProjectionExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "ProjectionExtension[T]":
         """Extends the given STAC Object with properties from the :stac-ext:`Projection
         Extension <projection>`.
 
@@ -250,12 +250,18 @@ def ext(obj: T) -> "ProjectionExtension[T]":
             pystac.ExtensionTypeError : If an invalid object type is passed.
         """
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(ProjectionExtension[T], ItemProjectionExtension(obj))
         elif isinstance(obj, pystac.Asset):
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
             return cast(ProjectionExtension[T], AssetProjectionExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
-                f"File extension does not apply to type {type(obj)}"
+                f"Projection extension does not apply to type {type(obj)}"
             )
 
     @staticmethod
diff --git a/pystac/extensions/raster.py b/pystac/extensions/raster.py
index 031940055..551474b17 100644
--- a/pystac/extensions/raster.py
+++ b/pystac/extensions/raster.py
@@ -4,7 +4,7 @@
 """
 
 import enum
-from typing import Any, Dict, Generic, Iterable, List, Optional, TypeVar, cast
+from typing import Any, Dict, Iterable, List, Optional
 
 import pystac
 from pystac.extensions.base import (
@@ -14,8 +14,6 @@
 )
 from pystac.utils import get_opt, get_required, map_opt
 
-T = TypeVar("T", pystac.Item, pystac.Asset)
-
 SCHEMA_URI = "https://stac-extensions.github.io/raster/v1.0.0/schema.json"
 
 BANDS_PROP = "raster:bands"
@@ -625,9 +623,7 @@ def to_dict(self) -> Dict[str, Any]:
         return self.properties
 
 
-class RasterExtension(
-    Generic[T], PropertiesExtension, ExtensionManagementMixin[pystac.Item]
-):
+class RasterExtension(PropertiesExtension, ExtensionManagementMixin[pystac.Item]):
     """An abstract class that can be used to extend the properties of an
     :class:`~pystac.Item` or :class:`~pystac.Asset` with properties from
     the :stac-ext:`Raster Extension <raster>`. This class is generic over
@@ -639,6 +635,25 @@ class RasterExtension(
     :class:`~ItemRasterExtension` to extend an :class:`~pystac.Item`).
     """
 
+    asset_href: str
+    """The ``href`` value of the :class:`~pystac.Asset` being extended."""
+
+    properties: Dict[str, Any]
+    """The :class:`~pystac.Asset` fields, including extension properties."""
+
+    additional_read_properties: Optional[Iterable[Dict[str, Any]]] = None
+    """If present, this will be a list containing 1 dictionary representing the
+    properties of the owning :class:`~pystac.Item`."""
+
+    def __init__(self, asset: pystac.Asset):
+        self.asset_href = asset.href
+        self.properties = asset.properties
+        if asset.owner and isinstance(asset.owner, pystac.Item):
+            self.additional_read_properties = [asset.owner.properties]
+
+    def __repr__(self) -> str:
+        return "<AssetRasterExtension Asset href={}>".format(self.asset_href)
+
     def apply(self, bands: List[RasterBand]) -> None:
         """Applies raster extension properties to the extended :class:`pystac.Item` or
         :class:`pystac.Asset`.
@@ -673,10 +688,22 @@ def _get_bands(self) -> Optional[List[RasterBand]]:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "RasterExtension[T]":
+    @classmethod
+    def ext(cls, obj: pystac.Asset, add_if_missing: bool = False) -> "RasterExtension":
+        """Extends the given STAC Object with properties from the :stac-ext:`Raster
+        Extension <raster>`.
+
+        This extension can be applied to instances of :class:`~pystac.Asset`.
+
+        Raises:
+
+            pystac.ExtensionTypeError : If an invalid object type is passed.
+        """
         if isinstance(obj, pystac.Asset):
-            return cast(RasterExtension[T], AssetRasterExtension(obj))
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
+            return cls(obj)
         else:
             raise pystac.ExtensionTypeError(
                 f"Raster extension does not apply to type {type(obj)}"
@@ -687,35 +714,6 @@ def summaries(obj: pystac.Collection) -> "SummariesRasterExtension":
         return SummariesRasterExtension(obj)
 
 
-class AssetRasterExtension(RasterExtension[pystac.Asset]):
-    """A concrete implementation of :class:`RasterExtension` on an :class:`~pystac.Asset`
-    that extends the Asset fields to include properties defined in the
-    :stac-ext:`Raster Extension <raster>`.
-
-    This class should generally not be instantiated directly. Instead, call
-    :meth:`RasterExtension.ext` on an :class:`~pystac.Asset` to extend it.
-    """
-
-    asset_href: str
-    """The ``href`` value of the :class:`~pystac.Asset` being extended."""
-
-    properties: Dict[str, Any]
-    """The :class:`~pystac.Asset` fields, including extension properties."""
-
-    additional_read_properties: Optional[Iterable[Dict[str, Any]]] = None
-    """If present, this will be a list containing 1 dictionary representing the
-    properties of the owning :class:`~pystac.Item`."""
-
-    def __init__(self, asset: pystac.Asset):
-        self.asset_href = asset.href
-        self.properties = asset.properties
-        if asset.owner and isinstance(asset.owner, pystac.Item):
-            self.additional_read_properties = [asset.owner.properties]
-
-    def __repr__(self) -> str:
-        return "<AssetRasterExtension Asset href={}>".format(self.asset_href)
-
-
 class SummariesRasterExtension(SummariesExtension):
     """A concrete implementation of :class:`~SummariesExtension` that extends
     the ``summaries`` field of a :class:`~pystac.Collection` to include properties
diff --git a/pystac/extensions/sar.py b/pystac/extensions/sar.py
index 089a567dc..0f07213ea 100644
--- a/pystac/extensions/sar.py
+++ b/pystac/extensions/sar.py
@@ -304,15 +304,21 @@ def observation_direction(self, v: Optional[ObservationDirection]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "SarExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "SarExtension[T]":
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(SarExtension[T], ItemSarExtension(obj))
         elif isinstance(obj, pystac.Asset):
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
             return cast(SarExtension[T], AssetSarExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
-                f"File extension does not apply to type {type(obj)}"
+                f"SAR extension does not apply to type {type(obj)}"
             )
 
 
diff --git a/pystac/extensions/sat.py b/pystac/extensions/sat.py
index 2f583fdfe..a84cb0b14 100644
--- a/pystac/extensions/sat.py
+++ b/pystac/extensions/sat.py
@@ -95,11 +95,17 @@ def relative_orbit(self, v: Optional[int]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "SatExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "SatExtension[T]":
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(SatExtension[T], ItemSatExtension(obj))
         elif isinstance(obj, pystac.Asset):
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
             return cast(SatExtension[T], AssetSatExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
diff --git a/pystac/extensions/scientific.py b/pystac/extensions/scientific.py
index 80d8a4e8a..fff9f3ce1 100644
--- a/pystac/extensions/scientific.py
+++ b/pystac/extensions/scientific.py
@@ -224,8 +224,8 @@ def remove_publication(self, publication: Optional[Publication] = None) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "ScientificExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "ScientificExtension[T]":
         """Extends the given STAC Object with properties from the :stac-ext:`Scientific
         Extension <scientific>`.
 
@@ -237,8 +237,14 @@ def ext(obj: T) -> "ScientificExtension[T]":
             pystac.ExtensionTypeError : If an invalid object type is passed.
         """
         if isinstance(obj, pystac.Collection):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(ScientificExtension[T], CollectionScientificExtension(obj))
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(ScientificExtension[T], ItemScientificExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
diff --git a/pystac/extensions/timestamps.py b/pystac/extensions/timestamps.py
index 211049900..f4de30851 100644
--- a/pystac/extensions/timestamps.py
+++ b/pystac/extensions/timestamps.py
@@ -116,11 +116,17 @@ def unpublished(self, v: Optional[Datetime]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "TimestampsExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "TimestampsExtension[T]":
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(TimestampsExtension[T], ItemTimestampsExtension(obj))
         elif isinstance(obj, pystac.Asset):
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
             return cast(TimestampsExtension[T], AssetTimestampsExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
diff --git a/pystac/extensions/version.py b/pystac/extensions/version.py
index 00436f6b8..ac01dbdc2 100644
--- a/pystac/extensions/version.py
+++ b/pystac/extensions/version.py
@@ -195,8 +195,8 @@ def successor(self, item_or_collection: Optional[T]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "VersionExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "VersionExtension[T]":
         """Extends the given STAC Object with properties from the :stac-ext:`Versioning
         Indicators Extension <version>`.
 
@@ -208,8 +208,14 @@ def ext(obj: T) -> "VersionExtension[T]":
             pystac.ExtensionTypeError : If an invalid object type is passed.
         """
         if isinstance(obj, pystac.Collection):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(VersionExtension[T], CollectionVersionExtension(obj))
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(VersionExtension[T], ItemVersionExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
diff --git a/pystac/extensions/view.py b/pystac/extensions/view.py
index 1fd0fa5b4..6438a2cb0 100644
--- a/pystac/extensions/view.py
+++ b/pystac/extensions/view.py
@@ -143,8 +143,8 @@ def sun_elevation(self, v: Optional[float]) -> None:
     def get_schema_uri(cls) -> str:
         return SCHEMA_URI
 
-    @staticmethod
-    def ext(obj: T) -> "ViewExtension[T]":
+    @classmethod
+    def ext(cls, obj: T, add_if_missing: bool = False) -> "ViewExtension[T]":
         """Extends the given STAC Object with properties from the :stac-ext:`View
         Geometry Extension <scientific>`.
 
@@ -156,8 +156,14 @@ def ext(obj: T) -> "ViewExtension[T]":
             pystac.ExtensionTypeError : If an invalid object type is passed.
         """
         if isinstance(obj, pystac.Item):
+            if add_if_missing:
+                cls.add_to(obj)
+            cls.validate_has_extension(obj)
             return cast(ViewExtension[T], ItemViewExtension(obj))
         elif isinstance(obj, pystac.Asset):
+            if add_if_missing and isinstance(obj.owner, pystac.Item):
+                cls.add_to(obj.owner)
+            cls.validate_has_extension(obj)
             return cast(ViewExtension[T], AssetViewExtension(obj))
         else:
             raise pystac.ExtensionTypeError(
diff --git a/tests/data-files/datacube/item.json b/tests/data-files/datacube/item.json
new file mode 100644
index 000000000..ddcd32e04
--- /dev/null
+++ b/tests/data-files/datacube/item.json
@@ -0,0 +1,120 @@
+{
+    "stac_version": "1.0.0-rc.1",
+    "stac_extensions": [
+        "https://stac-extensions.github.io/datacube/v1.0.0/schema.json"
+    ],
+    "id": "datacube-123",
+    "type": "Feature",
+    "geometry": {
+        "type": "Polygon",
+        "coordinates": [
+            [
+                [
+                    -122.308150179,
+                    37.488035566
+                ],
+                [
+                    -122.597502109,
+                    37.538869539
+                ],
+                [
+                    -122.576687533,
+                    37.613537207
+                ],
+                [
+                    -122.2880486,
+                    37.562818007
+                ],
+                [
+                    -122.308150179,
+                    37.488035566
+                ]
+            ]
+        ]
+    },
+    "bbox": [
+        -122.59750209,
+        37.48803556,
+        -122.2880486,
+        37.613537207
+    ],
+    "properties": {
+        "title": "Multi-dimensional data cube 123 in a STAC Item.",
+        "datetime": "2016-05-03T13:21:30.040Z",
+        "cube:dimensions": {
+            "x": {
+                "type": "spatial",
+                "axis": "x",
+                "extent": [
+                    -122.59750209,
+                    -122.2880486
+                ],
+                "reference_system": 4326
+            },
+            "y": {
+                "type": "spatial",
+                "axis": "y",
+                "extent": [
+                    37.48803556,
+                    37.613537207
+                ],
+                "reference_system": 4326
+            },
+            "pressure_levels": {
+                "type": "spatial",
+                "axis": "z",
+                "extent": [
+                    0,
+                    1000
+                ],
+                "step": 100,
+                "unit": "Pa"
+            },
+            "metered_levels": {
+                "type": "spatial",
+                "axis": "z",
+                "values": [
+                    0,
+                    10,
+                    25,
+                    50,
+                    100,
+                    1000
+                ],
+                "unit": "m"
+            },
+            "time": {
+                "type": "temporal",
+                "values": [
+                    "2016-05-03T13:21:30.040Z"
+                ]
+            },
+            "spectral": {
+                "type": "bands",
+                "values": [
+                    "red",
+                    "green",
+                    "blue"
+                ]
+            }
+        }
+    },
+    "assets": {
+        "data": {
+            "href": "http://cool-sat.com/catalog/datacube-123/data.nc",
+            "type": "application/netcdf",
+            "title": "netCDF Data cube"
+        },
+        "thumbnail": {
+            "href": "http://cool-sat.com/catalog/datacube-123/thumbnail.png",
+            "type": "image/png",
+            "title": "Thumbnail"
+        }
+    },
+    "links": [
+        {
+            "rel": "self",
+            "href": "http://cool-sat.com/catalog/datacube-123/example-item.json"
+        }
+    ]
+}
\ No newline at end of file
diff --git a/tests/data-files/sar/sentinel-1.json b/tests/data-files/sar/sentinel-1.json
new file mode 100644
index 000000000..42adcde3b
--- /dev/null
+++ b/tests/data-files/sar/sentinel-1.json
@@ -0,0 +1,107 @@
+{
+    "type": "Feature",
+    "stac_version": "1.0.0-rc.1",
+    "stac_extensions": [
+        "https://stac-extensions.github.io/sar/v1.0.0/schema.json"
+    ],
+    "id": "sentinel-1-example",
+    "properties": {
+        "datetime": "2018-11-03T23:58:55.617217Z",
+        "start_datetime": "2018-11-03T23:58:55.121559Z",
+        "end_datetime": "2018-11-03T23:59:55.112875Z",
+        "platform": "sentinel-1a",
+        "constellation": "sentinel-1",
+        "instruments": [
+            "c-sar"
+        ],
+        "sar:instrument_mode": "EW",
+        "sar:polarizations": [
+            "HH"
+        ],
+        "sar:resolution_range": 50,
+        "sar:resolution_azimuth": 50,
+        "sar:pixel_spacing_range": 25,
+        "sar:pixel_spacing_azimuth": 25,
+        "sar:looks_range": 3,
+        "sar:looks_azimuth": 1,
+        "sar:looks_equivalent_number": 2.7,
+        "sar:frequency_band": "C",
+        "sar:center_frequency": 5.405,
+        "sar:product_type": "GRD"
+    },
+    "geometry": {
+        "type": "Polygon",
+        "coordinates": [
+            [
+                [
+                    -67.071648,
+                    -64.72924
+                ],
+                [
+                    -65.087479,
+                    -56.674374
+                ],
+                [
+                    -68.033211,
+                    -51.105831
+                ],
+                [
+                    -70.275032,
+                    -59.805672
+                ],
+                [
+                    -67.071648,
+                    -64.72924
+                ]
+            ]
+        ]
+    },
+    "links": [
+        {
+            "rel": "root",
+            "href": "../../catalog.json",
+            "type": "application/json"
+        },
+        {
+            "rel": "parent",
+            "href": "../collection.json",
+            "type": "application/json"
+        }
+    ],
+    "assets": {
+        "noises": {
+            "href": "https://example.com/collections/sentinel-1/items/annotation/calibration/noise-s1a-ew-grd-hh-20181103t235855-20181103t235955-024430-02ad5d-001.xml",
+            "type": "text/xml",
+            "title": "Calibration Schema"
+        },
+        "calibrations": {
+            "href": "https://example.com/collections/sentinel-1/items/annotation/calibration/calibration-s1a-ew-grd-hh-20181103t235855-20181103t235955-024430-02ad5d-001.xml",
+            "type": "text/xml",
+            "title": "Noise Schema"
+        },
+        "products": {
+            "href": "https://example.com/collections/sentinel-1/items/annotation/s1a-ew-grd-hh-20181103t235855-20181103t235955-024430-02ad5d-001.xml",
+            "type": "text/xml",
+            "title": "Product Schema"
+        },
+        "measurement": {
+            "href": "https://example.com/collections/sentinel-1/items/measurement/s1a-ew-grd-hh-20181103t235855-20181103t235955-024430-02ad5d-001.tiff",
+            "type": "image/tiff",
+            "title": "Measurements",
+            "sar:polarizations": [
+                "HH"
+            ]
+        },
+        "thumbnail": {
+            "href": "https://example.com/collections/sentinel-1/items/preview/quick-look.png",
+            "type": "image/png",
+            "title": "Thumbnail"
+        }
+    },
+    "bbox": [
+        -70.275032,
+        -64.72924,
+        -65.087479,
+        -51.105831
+    ]
+}
\ No newline at end of file
diff --git a/tests/data-files/sat/sentinel-1.json b/tests/data-files/sat/sentinel-1.json
new file mode 100644
index 000000000..fa93b0112
--- /dev/null
+++ b/tests/data-files/sat/sentinel-1.json
@@ -0,0 +1,126 @@
+{
+    "stac_version": "1.0.0-rc.1",
+    "stac_extensions": [
+        "https://stac-extensions.github.io/sar/v1.0.0/schema.json",
+        "https://stac-extensions.github.io/sat/v1.0.0/schema.json"
+    ],
+    "id": "S1A_IW_SLC__1SDV_20150305T051937_20150305T052005_004892_006196_ABBB",
+    "type": "Feature",
+    "bbox": [
+        9.768469,
+        40.479584,
+        13.182633,
+        42.516747
+    ],
+    "geometry": {
+        "type": "Polygon",
+        "coordinates": [
+            [
+                [
+                    12.756503,
+                    40.479584
+                ],
+                [
+                    9.768469,
+                    40.877575
+                ],
+                [
+                    10.115331,
+                    42.516747
+                ],
+                [
+                    13.182633,
+                    42.119347
+                ],
+                [
+                    12.756503,
+                    40.479584
+                ]
+            ]
+        ]
+    },
+    "properties": {
+        "title": "Sentinel-1A SLC IW SDV T95 2015-03-05T05:19:37/2015-03-05T05:20:05",
+        "datetime": "2015-03-05T05:19:37.9237880Z",
+        "start_datetime": "2015-03-05T05:19:37.9237880Z",
+        "end_datetime": "2015-03-05T05:20:05.2359650Z",
+        "platform": "sentinel-1a",
+        "constellation": "sentinel-1",
+        "instruments": [
+            "c-sar"
+        ],
+        "sat:platform_international_designator": "2014-016A",
+        "sat:orbit_state": "descending",
+        "sat:absolute_orbit": 4892,
+        "sat:relative_orbit": 95,
+        "sat:anx_datetime": "2015-03-05T04:41:46.5788740Z",
+        "sar:instrument_mode": "IW",
+        "sar:polarizations": [
+            "VV",
+            "VH"
+        ],
+        "sar:resolution_range": 3.5,
+        "sar:resolution_azimuth": 22,
+        "sar:pixel_spacing_range": 2.3,
+        "sar:pixel_spacing_azimuth": 14.1,
+        "sar:looks_range": 1,
+        "sar:looks_azimuth": 1,
+        "sar:looks_equivalent_number": 1,
+        "sar:frequency_band": "C",
+        "sar:center_frequency": 5.405,
+        "sar:product_type": "SLC"
+    },
+    "assets": {
+        "noises_iw1_vh": {
+            "href": "./annotation/calibration/noise-s1a-iw1-slc-vh-20150305t051939-20150305t052005-004892-006196-001.xml",
+            "title": "Calibration Schema",
+            "type": "text/xml",
+            "sar:polarizations": [
+                "VH"
+            ]
+        },
+        "calibrations_iw1_vh": {
+            "href": "./annotation/calibration/calibration-s1a-iw1-slc-vh-20150305t051939-20150305t052005-004892-006196-001.xml",
+            "title": "Noise Schema",
+            "type": "text/xml",
+            "sar:polarizations": [
+                "VH"
+            ]
+        },
+        "products_iw1_vh": {
+            "href": "./annotation/s1a-iw1-slc-vh-20150305t051939-20150305t052005-004892-006196-001.xml",
+            "title": "Product Schema",
+            "type": "text/xml",
+            "sar:polarizations": [
+                "VH"
+            ]
+        },
+        "measurement_iw1_vh": {
+            "href": "./measurement/s1a-iw1-slc-vh-20150305t051939-20150305t052005-004892-006196-001.tiff",
+            "title": "Measurements",
+            "type": "image/tiff",
+            "sar:polarizations": [
+                "VH"
+            ]
+        },
+        "thumbnail": {
+            "href": "./preview/quick-look.png",
+            "title": "Thumbnail",
+            "type": "image/png"
+        }
+    },
+    "links": [
+        {
+            "rel": "self",
+            "href": "https://example.com/collections/sentinel-1/items/S1A_EW_GRDM_1SSH_20181103T235855_20181103T235955_024430_02AD5D_5616"
+        },
+        {
+            "rel": "parent",
+            "href": "https://example.com/collections/sentinel-1"
+        },
+        {
+            "rel": "root",
+            "href": "https://example.com/collections"
+        }
+    ]
+}
\ No newline at end of file
diff --git a/tests/data-files/scientific/collection.json b/tests/data-files/scientific/collection.json
new file mode 100644
index 000000000..59da6a7f6
--- /dev/null
+++ b/tests/data-files/scientific/collection.json
@@ -0,0 +1,63 @@
+{
+    "stac_version": "1.0.0-rc.1",
+    "stac_extensions": [
+        "https://stac-extensions.github.io/scientific/v1.0.0/schema.json"
+    ],
+    "id": "MERRAclim",
+    "title": "MERRAclim, a high-resolution global dataset of remotely sensed bioclimatic variables for ecological modelling.",
+    "description": "Species Distribution Models (SDMs) combine information on the geographic occurrence of species with environmental layers to estimate distributional ranges and have been extensively implemented to answer a wide array of applied ecological questions. Unfortunately, most global datasets available to parameterize SDMs consist of spatially interpolated climate surfaces obtained from ground weather station data and have omitted the Antarctic continent, a landmass covering c. 20% of the Southern Hemisphere and increasingly showing biological effects of global change. Here we introduce MERRAclim, a global set of satellite-based bioclimatic variables including Antarctica for the first time. MERRAclim consists of three datasets of 19 bioclimatic variables that have been built for each of the last three decades (1980s, 1990s and 2000s) using hourly data of 2 m temperature and specific humidity. We provide MERRAclim at three spatial resolutions (10 arc-minutes, 5 arc-minutes and 2.5 arc-minutes). These reanalysed data are comparable to widely used datasets based on ground station interpolations, but allow extending their geographical reach and SDM building in previously uncovered regions of the globe.",
+    "type": "Collection",
+    "keywords": [
+        "bioclimatic",
+        "MERRAclim",
+        "macroecology",
+        "biogeography"
+    ],
+    "license": "CC0-1.0",
+    "extent": {
+        "spatial": {
+            "bbox": [
+                [
+                    -180,
+                    -90,
+                    180,
+                    90
+                ]
+            ]
+        },
+        "temporal": {
+            "interval": [
+                [
+                    "1980-01-01T00:00:00Z",
+                    "2009-12-31T23:59:59Z"
+                ]
+            ]
+        }
+    },
+    "sci:doi": "10.5061/dryad.s2v81.2",
+    "sci:citation": "Vega GC, Pertierra LR, Olalla-Tárraga MÁ (2017) Data from: MERRAclim, a high-resolution global dataset of remotely sensed bioclimatic variables for ecological modelling. Dryad Digital Repository.",
+    "sci:publications": [
+        {
+            "doi": "10.1038/sdata.2017.78",
+            "citation": "Vega GC, Pertierra LR, Olalla-Tárraga MÁ (2017) MERRAclim, a high-resolution global dataset of remotely sensed bioclimatic variables for ecological modelling. Scientific Data 4: 170078."
+        }
+    ],
+    "links": [
+        {
+            "rel": "self",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/collection.json"
+        },
+        {
+            "rel": "item",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/item.json"
+        },
+        {
+            "rel": "root",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/collection.json"
+        },
+        {
+            "rel": "cite-as",
+            "href": "https://doi.org/10.5061/dryad.s2v81.2"
+        }
+    ]
+}
\ No newline at end of file
diff --git a/tests/data-files/scientific/item.json b/tests/data-files/scientific/item.json
new file mode 100644
index 000000000..f3e103ee7
--- /dev/null
+++ b/tests/data-files/scientific/item.json
@@ -0,0 +1,80 @@
+{
+    "stac_version": "1.0.0-rc.1",
+    "stac_extensions": [
+        "https://stac-extensions.github.io/scientific/v1.0.0/schema.json"
+    ],
+    "id": "MERRAclim.2_5m_min_80s",
+    "type": "Feature",
+    "geometry": {
+        "type": "Polygon",
+        "coordinates": [
+            [
+                [
+                    -180,
+                    -90
+                ],
+                [
+                    180,
+                    -90
+                ],
+                [
+                    180,
+                    90
+                ],
+                [
+                    -180,
+                    90
+                ],
+                [
+                    -180,
+                    -90
+                ]
+            ]
+        ]
+    },
+    "bbox": [
+        -180,
+        -90,
+        180,
+        90
+    ],
+    "properties": {
+        "title": "MERRAclim. 2_5m_min_80s",
+        "description": "MERRAclim Dataset. 19 global bioclimatic variables from the 1980s decade at 2.5 arcminutes resolution in GEOtiff format. The humidity version used is the min. The variables have been built using the same protocol as WorldClim with data from MERRA. Temperature layers (BIO1-BIO11) are in degree Celsius multiplied by 10, humidity layers (BIO12-BIO19) are in kg of water/kg of air multiplied by 100000.",
+        "datetime": "1985-07-01T00:00:00Z",
+        "start_datetime": "1980-01-01T00:00:00Z",
+        "end_datetime": "1989-12-31T23:59:59Z",
+        "sci:doi": "10.5061/dryad.s2v81.2/27.2",
+        "sci:publications": [
+            {
+                "doi": "10.5061/dryad.s2v81.2",
+                "citation": "Vega GC, Pertierra LR, Olalla-Tárraga MÁ (2017) Data from: MERRAclim, a high-resolution global dataset of remotely sensed bioclimatic variables for ecological modelling. Dryad Digital Repository."
+            },
+            {
+                "doi": "10.1038/sdata.2017.78",
+                "citation": "Vega GC, Pertierra LR, Olalla-Tárraga MÁ (2017) MERRAclim, a high-resolution global dataset of remotely sensed bioclimatic variables for ecological modelling. Scientific Data 4: 170078."
+            }
+        ]
+    },
+    "links": [
+        {
+            "rel": "self",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/item.json"
+        },
+        {
+            "rel": "root",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/catalog.json"
+        },
+        {
+            "rel": "cite-as",
+            "href": "https://doi.org/10.5061/dryad.s2v81.2/27.2"
+        }
+    ],
+    "assets": {
+        "primary": {
+            "href": "https://datadryad.org/stash/downloads/file_stream/100467",
+            "type": "application/zip",
+            "title": "MERRAclim. 2_5m_min_80s"
+        }
+    }
+}
\ No newline at end of file
diff --git a/tests/data-files/version/collection.json b/tests/data-files/version/collection.json
new file mode 100644
index 000000000..987e5f15b
--- /dev/null
+++ b/tests/data-files/version/collection.json
@@ -0,0 +1,51 @@
+{
+    "stac_version": "1.0.0-rc.1",
+    "stac_extensions": [
+        "https://stac-extensions.github.io/version/v1.0.0/schema.json"
+    ],
+    "id": "merraclim",
+    "type": "Collection",
+    "title": "MERRAclim",
+    "description": "A high-resolution global dataset of remotely sensed bioclimatic variables for ecological modelling.",
+    "license": "CC0-1.0",
+    "version": "1",
+    "deprecated": true,
+    "extent": {
+        "spatial": {
+            "bbox": [
+                [
+                    -180,
+                    -90,
+                    180,
+                    90
+                ]
+            ]
+        },
+        "temporal": {
+            "interval": [
+                [
+                    "1980-01-01T00:00:00Z",
+                    "2009-12-31T23:59:59Z"
+                ]
+            ]
+        }
+    },
+    "links": [
+        {
+            "rel": "self",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/v1/collection.json"
+        },
+        {
+            "rel": "item",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/v1/item.json"
+        },
+        {
+            "rel": "root",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/catalog.json"
+        },
+        {
+            "rel": "latest-version",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/v2/collection.json"
+        }
+    ]
+}
\ No newline at end of file
diff --git a/tests/data-files/version/item.json b/tests/data-files/version/item.json
new file mode 100644
index 000000000..919f473fe
--- /dev/null
+++ b/tests/data-files/version/item.json
@@ -0,0 +1,77 @@
+{
+    "stac_version": "1.0.0-rc.1",
+    "stac_extensions": [
+        "https://stac-extensions.github.io/version/v1.0.0/schema.json"
+    ],
+    "id": "MERRAclim.2_5m_min_80s",
+    "type": "Feature",
+    "geometry": {
+        "type": "Polygon",
+        "coordinates": [
+            [
+                [
+                    -180,
+                    -90
+                ],
+                [
+                    180,
+                    -90
+                ],
+                [
+                    180,
+                    90
+                ],
+                [
+                    -180,
+                    90
+                ],
+                [
+                    -180,
+                    -90
+                ]
+            ]
+        ]
+    },
+    "bbox": [
+        -180,
+        -90,
+        180,
+        90
+    ],
+    "properties": {
+        "version": "1",
+        "title": "MERRAclim. 2_5m_min_80s",
+        "description": "MERRAclim Dataset. 19 global bioclimatic variables from the 1980s decade at 2.5 arcminutes resolution in GEOtiff format. The humidity version used is the min. The variables have been built using the same protocol as WorldClim with data from MERRA. Temperature layers (BIO1-BIO11) are in degree Celsius multiplied by 10, humidity layers (BIO12-BIO19) are in kg of water/kg of air multiplied by 100000.",
+        "datetime": "1985-07-01T00:00:00Z"
+    },
+    "collection": "merraclim",
+    "links": [
+        {
+            "rel": "self",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/v1/item.json"
+        },
+        {
+            "rel": "collection",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/v1/collection.json"
+        },
+        {
+            "rel": "parent",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/v1/collection.json"
+        },
+        {
+            "rel": "root",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/catalog.json"
+        },
+        {
+            "rel": "latest-version",
+            "href": "https://datadryad.org/resource/doi:10.5061/dryad.s2v81/v2/item.json"
+        }
+    ],
+    "assets": {
+        "primary": {
+            "href": "https://datadryad.org/stash/downloads/file_stream/100467",
+            "type": "application/zip",
+            "title": "MERRAclim. 2_5m_min_80s"
+        }
+    }
+}
\ No newline at end of file
diff --git a/tests/extensions/test_datacube.py b/tests/extensions/test_datacube.py
new file mode 100644
index 000000000..251bd7f83
--- /dev/null
+++ b/tests/extensions/test_datacube.py
@@ -0,0 +1,52 @@
+import unittest
+import pystac
+from pystac.extensions.datacube import DatacubeExtension
+
+from tests.utils import TestCases
+
+
+class DatacubeTest(unittest.TestCase):
+    def setUp(self) -> None:
+        self.maxDiff = None
+        self.example_uri = TestCases.get_path("data-files/datacube/item.json")
+
+    def test_validate_datacube(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.validate()
+
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(DatacubeExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = DatacubeExtension.ext(item)
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["data"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = DatacubeExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = DatacubeExtension.ext(ownerless_asset)
+
+    def test_item_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(DatacubeExtension.get_schema_uri())
+        self.assertNotIn(DatacubeExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = DatacubeExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(DatacubeExtension.get_schema_uri(), item.stac_extensions)
+
+    def test_asset_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(DatacubeExtension.get_schema_uri())
+        self.assertNotIn(DatacubeExtension.get_schema_uri(), item.stac_extensions)
+        asset = item.assets["data"]
+
+        _ = DatacubeExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(DatacubeExtension.get_schema_uri(), item.stac_extensions)
diff --git a/tests/extensions/test_eo.py b/tests/extensions/test_eo.py
index 8e68d230a..6cf3b0af8 100644
--- a/tests/extensions/test_eo.py
+++ b/tests/extensions/test_eo.py
@@ -264,3 +264,37 @@ def test_extend_invalid_object(self) -> None:
 
         with self.assertRaises(pystac.ExtensionTypeError):
             EOExtension.ext(link)  # type: ignore
+
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.PLAIN_ITEM)
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = EOExtension.ext(item)
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["thumbnail"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = EOExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = EOExtension.ext(ownerless_asset)
+
+    def test_item_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.PLAIN_ITEM)
+        self.assertNotIn(EOExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = EOExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(EOExtension.get_schema_uri(), item.stac_extensions)
+
+    def test_asset_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.PLAIN_ITEM)
+        self.assertNotIn(EOExtension.get_schema_uri(), item.stac_extensions)
+        asset = item.assets["thumbnail"]
+
+        _ = EOExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(EOExtension.get_schema_uri(), item.stac_extensions)
diff --git a/tests/extensions/test_file.py b/tests/extensions/test_file.py
index 1d2e30212..35164b536 100644
--- a/tests/extensions/test_file.py
+++ b/tests/extensions/test_file.py
@@ -50,6 +50,7 @@ def test_apply(self) -> None:
 class FileTest(unittest.TestCase):
     FILE_ITEM_EXAMPLE_URI = TestCases.get_path("data-files/file/item.json")
     FILE_COLLECTION_EXAMPLE_URI = TestCases.get_path("data-files/file/collection.json")
+    PLAIN_ITEM = TestCases.get_path("data-files/item/sample-item.json")
 
     def setUp(self) -> None:
         self.maxDiff = None
@@ -188,3 +189,32 @@ def test_migrates_old_checksum(self) -> None:
             FileExtension.ext(item.assets["noises"]).checksum,
             "90e40210a30d1711e81a4b11ef67b28744321659",
         )
+
+    def test_extension_type_error(self) -> None:
+        item = pystac.Item.from_file(self.FILE_ITEM_EXAMPLE_URI)
+
+        with self.assertRaises(pystac.ExtensionTypeError):
+            _ = FileExtension.ext(item)  # type: ignore
+
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.PLAIN_ITEM)
+        asset = item.assets["thumbnail"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = FileExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+
+        _ = FileExtension.ext(ownerless_asset)
+
+    def test_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.PLAIN_ITEM)
+        asset = item.assets["thumbnail"]
+
+        self.assertNotIn(FileExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = FileExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(FileExtension.get_schema_uri(), item.stac_extensions)
diff --git a/tests/extensions/test_label.py b/tests/extensions/test_label.py
index fbee72ad1..ac3f84134 100644
--- a/tests/extensions/test_label.py
+++ b/tests/extensions/test_label.py
@@ -361,3 +361,27 @@ def test_merge_label_overviews_error(self) -> None:
 
         with self.assertRaises(AssertionError):
             _ = overview_1.merge_counts(overview_2)
+
+    def test_extension_type_error(self) -> None:
+        collection = pystac.Collection.from_file(
+            TestCases.get_path("data-files/collections/with-assets.json")
+        )
+        with self.assertRaises(pystac.ExtensionTypeError):
+            _ = LabelExtension.ext(collection)  # type: ignore
+
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.label_example_1_uri)
+        item.stac_extensions.remove(LabelExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = LabelExtension.ext(item)
+
+    def test_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.label_example_1_uri)
+        item.stac_extensions.remove(LabelExtension.get_schema_uri())
+        self.assertNotIn(LabelExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = LabelExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(LabelExtension.get_schema_uri(), item.stac_extensions)
diff --git a/tests/extensions/test_pointcloud.py b/tests/extensions/test_pointcloud.py
index 9bad4a440..1a71cd057 100644
--- a/tests/extensions/test_pointcloud.py
+++ b/tests/extensions/test_pointcloud.py
@@ -293,3 +293,40 @@ class RandomObject:
 
         with self.assertRaises(ExtensionTypeError):
             PointcloudExtension.ext(RandomObject())  # type: ignore
+
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        plain_item_uri = TestCases.get_path("data-files/item/sample-item.json")
+        item = pystac.Item.from_file(plain_item_uri)
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = PointcloudExtension.ext(item)
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["thumbnail"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = PointcloudExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = PointcloudExtension.ext(ownerless_asset)
+
+    def test_item_ext_add_to(self) -> None:
+        plain_item_uri = TestCases.get_path("data-files/item/sample-item.json")
+        item = pystac.Item.from_file(plain_item_uri)
+        self.assertNotIn(PointcloudExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = PointcloudExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(PointcloudExtension.get_schema_uri(), item.stac_extensions)
+
+    def test_asset_ext_add_to(self) -> None:
+        plain_item_uri = TestCases.get_path("data-files/item/sample-item.json")
+        item = pystac.Item.from_file(plain_item_uri)
+        self.assertNotIn(PointcloudExtension.get_schema_uri(), item.stac_extensions)
+        asset = item.assets["thumbnail"]
+
+        _ = PointcloudExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(PointcloudExtension.get_schema_uri(), item.stac_extensions)
diff --git a/tests/extensions/test_projection.py b/tests/extensions/test_projection.py
index a6c804aab..e28dc2e37 100644
--- a/tests/extensions/test_projection.py
+++ b/tests/extensions/test_projection.py
@@ -406,6 +406,43 @@ def test_transform(self) -> None:
         # Validate
         proj_item.validate()
 
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(ProjectionExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = ProjectionExtension.ext(item)
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["B8"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = ProjectionExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = ProjectionExtension.ext(ownerless_asset)
+
+    def test_item_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(ProjectionExtension.get_schema_uri())
+        self.assertNotIn(ProjectionExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = ProjectionExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(ProjectionExtension.get_schema_uri(), item.stac_extensions)
+
+    def test_asset_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(ProjectionExtension.get_schema_uri())
+        self.assertNotIn(ProjectionExtension.get_schema_uri(), item.stac_extensions)
+        asset = item.assets["B8"]
+
+        _ = ProjectionExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(ProjectionExtension.get_schema_uri(), item.stac_extensions)
+
 
 class ProjectionSummariesTest(unittest.TestCase):
     def setUp(self) -> None:
diff --git a/tests/extensions/test_raster.py b/tests/extensions/test_raster.py
index aeed0d9ba..825a6b86f 100644
--- a/tests/extensions/test_raster.py
+++ b/tests/extensions/test_raster.py
@@ -198,3 +198,27 @@ def test_asset_bands(self) -> None:
             item.assets["test"].properties["raster:bands"][0]["statistics"]["minimum"],
             1,
         )
+
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.PLANET_EXAMPLE_URI)
+        item.stac_extensions.remove(RasterExtension.get_schema_uri())
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["data"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = RasterExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = RasterExtension.ext(ownerless_asset)
+
+    def test_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.PLANET_EXAMPLE_URI)
+        item.stac_extensions.remove(RasterExtension.get_schema_uri())
+        asset = item.assets["data"]
+
+        _ = RasterExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(RasterExtension.get_schema_uri(), item.stac_extensions)
diff --git a/tests/extensions/test_sar.py b/tests/extensions/test_sar.py
index 2696eba39..23311bced 100644
--- a/tests/extensions/test_sar.py
+++ b/tests/extensions/test_sar.py
@@ -7,6 +7,7 @@
 import pystac
 from pystac.extensions import sar
 from pystac.extensions.sar import SarExtension
+from tests.utils import TestCases
 
 
 def make_item() -> pystac.Item:
@@ -24,6 +25,7 @@ class SarItemExtTest(unittest.TestCase):
     def setUp(self) -> None:
         super().setUp()
         self.item = make_item()
+        self.sentinel_example_uri = TestCases.get_path("data-files/sar/sentinel-1.json")
 
     def test_stac_extensions(self) -> None:
         self.assertTrue(SarExtension.has_extension(self.item))
@@ -141,6 +143,43 @@ def test_polarization_must_be_list(self) -> None:
                 product_type,
             )
 
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.sentinel_example_uri)
+        item.stac_extensions.remove(SarExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = SarExtension.ext(item)
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["measurement"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = SarExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = SarExtension.ext(ownerless_asset)
+
+    def test_item_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.sentinel_example_uri)
+        item.stac_extensions.remove(SarExtension.get_schema_uri())
+        self.assertNotIn(SarExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = SarExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(SarExtension.get_schema_uri(), item.stac_extensions)
+
+    def test_asset_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.sentinel_example_uri)
+        item.stac_extensions.remove(SarExtension.get_schema_uri())
+        self.assertNotIn(SarExtension.get_schema_uri(), item.stac_extensions)
+        asset = item.assets["measurement"]
+
+        _ = SarExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(SarExtension.get_schema_uri(), item.stac_extensions)
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/tests/extensions/test_sat.py b/tests/extensions/test_sat.py
index 50fdbda5a..d55fd3e9e 100644
--- a/tests/extensions/test_sat.py
+++ b/tests/extensions/test_sat.py
@@ -7,6 +7,7 @@
 import pystac
 from pystac.extensions import sat
 from pystac.extensions.sat import SatExtension
+from tests.utils import TestCases
 
 
 def make_item() -> pystac.Item:
@@ -25,6 +26,7 @@ class SatTest(unittest.TestCase):
     def setUp(self) -> None:
         super().setUp()
         self.item = make_item()
+        self.sentinel_example_uri = TestCases.get_path("data-files/sat/sentinel-1.json")
 
     def test_stac_extensions(self) -> None:
         self.assertTrue(SatExtension.has_extension(self.item))
@@ -90,7 +92,7 @@ def test_from_dict(self) -> None:
             "geometry": None,
             "links": [],
             "assets": {},
-            "stac_extensions": ["sat"],
+            "stac_extensions": [SatExtension.get_schema_uri()],
         }
         item = pystac.Item.from_dict(d)
         self.assertEqual(orbit_state, SatExtension.ext(item).orbit_state)
@@ -121,3 +123,40 @@ def test_clear_relative_orbit(self) -> None:
         SatExtension.ext(self.item).relative_orbit = None
         self.assertIsNone(SatExtension.ext(self.item).relative_orbit)
         self.item.validate()
+
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.sentinel_example_uri)
+        item.stac_extensions.remove(SatExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = SatExtension.ext(item)
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["measurement_iw1_vh"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = SatExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = SatExtension.ext(ownerless_asset)
+
+    def test_item_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.sentinel_example_uri)
+        item.stac_extensions.remove(SatExtension.get_schema_uri())
+        self.assertNotIn(SatExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = SatExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(SatExtension.get_schema_uri(), item.stac_extensions)
+
+    def test_asset_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.sentinel_example_uri)
+        item.stac_extensions.remove(SatExtension.get_schema_uri())
+        self.assertNotIn(SatExtension.get_schema_uri(), item.stac_extensions)
+        asset = item.assets["measurement_iw1_vh"]
+
+        _ = SatExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(SatExtension.get_schema_uri(), item.stac_extensions)
diff --git a/tests/extensions/test_scientific.py b/tests/extensions/test_scientific.py
index d7d05b2e1..99154c199 100644
--- a/tests/extensions/test_scientific.py
+++ b/tests/extensions/test_scientific.py
@@ -14,6 +14,7 @@
     ScientificRelType,
     remove_link,
 )
+from tests.utils import TestCases
 
 URL_TEMPLATE = "http://example.com/catalog/%s.json"
 
@@ -73,6 +74,7 @@ class ItemScientificExtensionTest(unittest.TestCase):
     def setUp(self) -> None:
         super().setUp()
         self.item = make_item()
+        self.example_item_uri = TestCases.get_path("data-files/scientific/item.json")
 
     def test_stac_extensions(self) -> None:
         self.assertTrue(ScientificExtension.has_extension(self.item))
@@ -206,6 +208,23 @@ def test_remove_all_publications_with_none(self) -> None:
         self.assertEqual(DOI_URL, links[0].target)
         self.item.validate()
 
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.example_item_uri)
+        item.stac_extensions.remove(ScientificExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = ScientificExtension.ext(item)
+
+    def test_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_item_uri)
+        item.stac_extensions.remove(ScientificExtension.get_schema_uri())
+        self.assertNotIn(ScientificExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = ScientificExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(ScientificExtension.get_schema_uri(), item.stac_extensions)
+
 
 def make_collection() -> pystac.Collection:
     asset_id = "my/thing"
@@ -227,6 +246,9 @@ class CollectionScientificExtensionTest(unittest.TestCase):
     def setUp(self) -> None:
         super().setUp()
         self.collection = make_collection()
+        self.example_collection_uri = TestCases.get_path(
+            "data-files/scientific/collection.json"
+        )
 
     def test_stac_extensions(self) -> None:
         self.assertTrue(ScientificExtension.has_extension(self.collection))
@@ -365,6 +387,25 @@ def test_remove_all_publications_with_none(self) -> None:
         self.assertEqual(DOI_URL, links[0].target)
         self.collection.validate()
 
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Collection does not include extension URI
+        collection = pystac.Collection.from_file(self.example_collection_uri)
+        collection.stac_extensions.remove(ScientificExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = ScientificExtension.ext(collection)
+
+    def test_ext_add_to(self) -> None:
+        collection = pystac.Collection.from_file(self.example_collection_uri)
+        collection.stac_extensions.remove(ScientificExtension.get_schema_uri())
+        self.assertNotIn(
+            ScientificExtension.get_schema_uri(), collection.stac_extensions
+        )
+
+        _ = ScientificExtension.ext(collection, add_if_missing=True)
+
+        self.assertIn(ScientificExtension.get_schema_uri(), collection.stac_extensions)
+
 
 class SummariesScientificTest(unittest.TestCase):
     def setUp(self) -> None:
diff --git a/tests/extensions/test_timestamps.py b/tests/extensions/test_timestamps.py
index 92e3e2805..6f1904965 100644
--- a/tests/extensions/test_timestamps.py
+++ b/tests/extensions/test_timestamps.py
@@ -185,3 +185,40 @@ def test_unpublished(self) -> None:
 
         # Validate
         timestamps_item.validate()
+
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(TimestampsExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = TimestampsExtension.ext(item)
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["blue"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = TimestampsExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = TimestampsExtension.ext(ownerless_asset)
+
+    def test_item_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(TimestampsExtension.get_schema_uri())
+        self.assertNotIn(TimestampsExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = TimestampsExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(TimestampsExtension.get_schema_uri(), item.stac_extensions)
+
+    def test_asset_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(TimestampsExtension.get_schema_uri())
+        self.assertNotIn(TimestampsExtension.get_schema_uri(), item.stac_extensions)
+        asset = item.assets["blue"]
+
+        _ = TimestampsExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(TimestampsExtension.get_schema_uri(), item.stac_extensions)
diff --git a/tests/extensions/test_version.py b/tests/extensions/test_version.py
index b5d8d7cc9..c3aabd860 100644
--- a/tests/extensions/test_version.py
+++ b/tests/extensions/test_version.py
@@ -33,6 +33,7 @@ class ItemVersionExtensionTest(unittest.TestCase):
     def setUp(self) -> None:
         super().setUp()
         self.item = make_item(2011)
+        self.example_item_uri = TestCases.get_path("data-files/version/item.json")
 
     def test_rel_types(self) -> None:
         self.assertEqual(str(VersionRelType.LATEST), "latest-version")
@@ -218,6 +219,23 @@ def test_multiple_link_setting(self) -> None:
         self.assertEqual(1, len(links))
         self.assertEqual(expected_href, links[0].get_href())
 
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.example_item_uri)
+        item.stac_extensions.remove(VersionExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = VersionExtension.ext(item)
+
+    def test_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_item_uri)
+        item.stac_extensions.remove(VersionExtension.get_schema_uri())
+        self.assertNotIn(VersionExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = VersionExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(VersionExtension.get_schema_uri(), item.stac_extensions)
+
 
 def make_collection(year: int) -> pystac.Collection:
     asset_id = f"my/collection/of/things/{year}"
@@ -243,6 +261,9 @@ class CollectionVersionExtensionTest(unittest.TestCase):
     def setUp(self) -> None:
         super().setUp()
         self.collection = make_collection(2011)
+        self.example_collection_uri = TestCases.get_path(
+            "data-files/version/collection.json"
+        )
 
     def test_stac_extensions(self) -> None:
         self.assertTrue(VersionExtension.has_extension(self.collection))
@@ -423,6 +444,23 @@ def test_multiple_link_setting(self) -> None:
         self.assertEqual(1, len(links))
         self.assertEqual(expected_href, links[0].get_href())
 
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Collection does not include extension URI
+        collection = pystac.Collection.from_file(self.example_collection_uri)
+        collection.stac_extensions.remove(VersionExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = VersionExtension.ext(collection)
+
+    def test_ext_add_to(self) -> None:
+        collection = pystac.Collection.from_file(self.example_collection_uri)
+        collection.stac_extensions.remove(VersionExtension.get_schema_uri())
+        self.assertNotIn(VersionExtension.get_schema_uri(), collection.stac_extensions)
+
+        _ = VersionExtension.ext(collection, add_if_missing=True)
+
+        self.assertIn(VersionExtension.get_schema_uri(), collection.stac_extensions)
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/tests/extensions/test_view.py b/tests/extensions/test_view.py
index 2b03529d3..ac6f10a5d 100644
--- a/tests/extensions/test_view.py
+++ b/tests/extensions/test_view.py
@@ -220,6 +220,43 @@ def test_sun_elevation(self) -> None:
         # Validate
         view_item.validate()
 
+    def test_extension_not_implemented(self) -> None:
+        # Should raise exception if Item does not include extension URI
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(ViewExtension.get_schema_uri())
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = ViewExtension.ext(item)
+
+        # Should raise exception if owning Item does not include extension URI
+        asset = item.assets["blue"]
+
+        with self.assertRaises(pystac.ExtensionNotImplemented):
+            _ = ViewExtension.ext(asset)
+
+        # Should succeed if Asset has no owner
+        ownerless_asset = pystac.Asset.from_dict(asset.to_dict())
+        _ = ViewExtension.ext(ownerless_asset)
+
+    def test_item_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(ViewExtension.get_schema_uri())
+        self.assertNotIn(ViewExtension.get_schema_uri(), item.stac_extensions)
+
+        _ = ViewExtension.ext(item, add_if_missing=True)
+
+        self.assertIn(ViewExtension.get_schema_uri(), item.stac_extensions)
+
+    def test_asset_ext_add_to(self) -> None:
+        item = pystac.Item.from_file(self.example_uri)
+        item.stac_extensions.remove(ViewExtension.get_schema_uri())
+        self.assertNotIn(ViewExtension.get_schema_uri(), item.stac_extensions)
+        asset = item.assets["blue"]
+
+        _ = ViewExtension.ext(asset, add_if_missing=True)
+
+        self.assertIn(ViewExtension.get_schema_uri(), item.stac_extensions)
+
 
 class ViewSummariestest(unittest.TestCase):
     def setUp(self) -> None: