diff --git a/superset/db_engine_specs/base.py b/superset/db_engine_specs/base.py
index efe7d68da2182..1e57996998183 100644
--- a/superset/db_engine_specs/base.py
+++ b/superset/db_engine_specs/base.py
@@ -472,7 +472,7 @@ def get_default_schema_for_query(
         Determining the correct schema is crucial for managing access to data, so please
         make sure you understand this logic when working on a new DB engine spec.
         """
-        # default schema varies on a per-query basis
+        # dynamic schema varies on a per-query basis
         if cls.supports_dynamic_schema:
             return query.schema
 
@@ -1061,25 +1061,27 @@ def adjust_engine_params(  # pylint: disable=unused-argument
         cls,
         uri: URL,
         connect_args: Dict[str, Any],
+        catalog: Optional[str],
         schema: Optional[str],
     ) -> Tuple[URL, Dict[str, Any]]:
         """
-        Return a modified URL with a new database component.
+        Return a new URL and ``connect_args`` for a specific catalog/schema.
 
-        The URI here represents the URI as entered when saving the database,
-        ``selected_schema`` is the schema currently active presumably in
-        the SQL Lab dropdown. Based on that, for some database engine,
-        we can return a new altered URI that connects straight to the
-        active schema, meaning the users won't have to prefix the object
-        names by the schema name.
+        This is used in SQL Lab, allowing users to select a schema from the list of
+        schemas available in a given database, and have the query run with that schema as
+        the default one.
 
-        Some databases engines have 2 level of namespacing: database and
-        schema (postgres, oracle, mssql, ...)
-        For those it's probably better to not alter the database
-        component of the URI with the schema name, it won't work.
+        For some databases (like MySQL, Presto, Snowflake) this requires modifying the
+        SQLAlchemy URI before creating the connection. For others (like Postgres), it
+        requires additional parameters in ``connect_args``.
 
-        Some database drivers like Presto accept '{catalog}/{schema}' in
-        the database component of the URL, that can be handled here.
+        When a DB engine spec implements this method it should also have the attribute
+        ``supports_dynamic_schema`` set to true, so that Superset knows in which schema a
+        given query is running in order to enforce permissions (see #23385 and #23401).
+
+        Currently, changing the catalog is not supported. The method acceps a catalog so
+        that when catalog support is added to Superse the interface remains the same. This
+        is important because DB engine specs can be installed from 3rd party packages.
         """
         return uri, connect_args
 
diff --git a/superset/db_engine_specs/drill.py b/superset/db_engine_specs/drill.py
index 5f7e9baf51170..ec7788ead2d07 100644
--- a/superset/db_engine_specs/drill.py
+++ b/superset/db_engine_specs/drill.py
@@ -75,6 +75,7 @@ def adjust_engine_params(
         cls,
         uri: URL,
         connect_args: Dict[str, Any],
+        catalog: Optional[str],
         schema: Optional[str],
     ) -> Tuple[URL, Dict[str, Any]]:
         if schema:
diff --git a/superset/db_engine_specs/hive.py b/superset/db_engine_specs/hive.py
index f70ff2db03dfd..792ef947350a1 100644
--- a/superset/db_engine_specs/hive.py
+++ b/superset/db_engine_specs/hive.py
@@ -264,6 +264,7 @@ def adjust_engine_params(
         cls,
         uri: URL,
         connect_args: Dict[str, Any],
+        catalog: Optional[str] = None,
         schema: Optional[str] = None,
     ) -> Tuple[URL, Dict[str, Any]]:
         if schema:
diff --git a/superset/db_engine_specs/mysql.py b/superset/db_engine_specs/mysql.py
index 572db3aab14a4..e5ff964f868da 100644
--- a/superset/db_engine_specs/mysql.py
+++ b/superset/db_engine_specs/mysql.py
@@ -195,6 +195,7 @@ def adjust_engine_params(
         cls,
         uri: URL,
         connect_args: Dict[str, Any],
+        catalog: Optional[str] = None,
         schema: Optional[str] = None,
     ) -> Tuple[URL, Dict[str, Any]]:
         if schema:
diff --git a/superset/db_engine_specs/postgres.py b/superset/db_engine_specs/postgres.py
index 3999c98e64967..7555b660116b5 100644
--- a/superset/db_engine_specs/postgres.py
+++ b/superset/db_engine_specs/postgres.py
@@ -154,6 +154,7 @@ def adjust_engine_params(
         cls,
         uri: URL,
         connect_args: Dict[str, Any],
+        catalog: Optional[str] = None,
         schema: Optional[str] = None,
     ) -> Tuple[URL, Dict[str, Any]]:
         if not schema:
diff --git a/superset/db_engine_specs/presto.py b/superset/db_engine_specs/presto.py
index 4004483abf52f..c0b4f2c6dd881 100644
--- a/superset/db_engine_specs/presto.py
+++ b/superset/db_engine_specs/presto.py
@@ -305,6 +305,7 @@ def adjust_engine_params(
         cls,
         uri: URL,
         connect_args: Dict[str, Any],
+        catalog: Optional[str] = None,
         schema: Optional[str] = None,
     ) -> Tuple[URL, Dict[str, Any]]:
         database = uri.database
diff --git a/superset/db_engine_specs/snowflake.py b/superset/db_engine_specs/snowflake.py
index f3bff7021cf6b..033b637e48d1d 100644
--- a/superset/db_engine_specs/snowflake.py
+++ b/superset/db_engine_specs/snowflake.py
@@ -139,6 +139,7 @@ def adjust_engine_params(
         cls,
         uri: URL,
         connect_args: Dict[str, Any],
+        catalog: Optional[str] = None,
         schema: Optional[str] = None,
     ) -> Tuple[URL, Dict[str, Any]]:
         database = uri.database
diff --git a/superset/models/core.py b/superset/models/core.py
index 45973e44d9061..d7a38cdc033a5 100755
--- a/superset/models/core.py
+++ b/superset/models/core.py
@@ -432,11 +432,29 @@ def _get_sqla_engine(
             params["poolclass"] = NullPool
         connect_args = params.get("connect_args", {})
 
+        # The ``adjust_database_uri`` method was renamed to ``adjust_engine_params`` and
+        # had its signature changed in order to support more DB engine specs. Since DB
+        # engine specs can be released as 3rd party modules we want to make sure the old
+        # method is still supported so we don't introduce a breaking change.
+        if hasattr(self.db_engine_spec, "adjust_database_uri"):
+            sqlalchemy_url = self.db_engine_spec.adjust_database_uri(
+                sqlalchemy_url,
+                schema,
+            )
+            logger.warning(
+                "DB engine spec %s implements the method `adjust_database_uri`, which is "
+                "deprecated and will be removed in version 3.0. Please update it to "
+                "implement `adjust_engine_params` instead.",
+                self.db_engine_spec,
+            )
+
         sqlalchemy_url, connect_args = self.db_engine_spec.adjust_engine_params(
-            sqlalchemy_url,
-            connect_args,
-            schema,
+            uri=sqlalchemy_url,
+            connect_args=connect_args,
+            catalog=None,
+            schema=schema,
         )
+
         effective_username = self.get_effective_user(sqlalchemy_url)
         # If using MySQL or Presto for example, will set url.username
         # If using Hive, will not do anything yet since that relies on a
diff --git a/tests/unit_tests/db_engine_specs/test_postgres.py b/tests/unit_tests/db_engine_specs/test_postgres.py
index 828f155cc9208..fef864795962e 100644
--- a/tests/unit_tests/db_engine_specs/test_postgres.py
+++ b/tests/unit_tests/db_engine_specs/test_postgres.py
@@ -141,7 +141,7 @@ def test_adjust_engine_params() -> None:
 
     uri = make_url("postgres://user:password@host/catalog")
 
-    assert PostgresEngineSpec.adjust_engine_params(uri, {}, "secret") == (
+    assert PostgresEngineSpec.adjust_engine_params(uri, {}, None, "secret") == (
         uri,
         {"options": "-csearch_path=secret"},
     )
@@ -149,6 +149,7 @@ def test_adjust_engine_params() -> None:
     assert PostgresEngineSpec.adjust_engine_params(
         uri,
         {"foo": "bar", "options": "-csearch_path=default -c debug=1"},
+        None,
         "secret",
     ) == (
         uri,