diff --git a/pandas/tests/frame/methods/test_append.py b/pandas/tests/frame/methods/test_append.py
index 133e8c03fab3d..c08a77d00a96d 100644
--- a/pandas/tests/frame/methods/test_append.py
+++ b/pandas/tests/frame/methods/test_append.py
@@ -7,6 +7,18 @@
 
 
 class TestDataFrameAppend:
+    @pytest.mark.parametrize("klass", [Series, DataFrame])
+    def test_append_multiindex(self, multiindex_dataframe_random_data, klass):
+        obj = multiindex_dataframe_random_data
+        if klass is Series:
+            obj = obj["A"]
+
+        a = obj[:5]
+        b = obj[5:]
+
+        result = a.append(b)
+        tm.assert_equal(result, obj)
+
     def test_append_empty_list(self):
         # GH 28769
         df = DataFrame()
diff --git a/pandas/tests/frame/test_convert.py b/pandas/tests/frame/methods/test_convert.py
similarity index 100%
rename from pandas/tests/frame/test_convert.py
rename to pandas/tests/frame/methods/test_convert.py
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index bbcc286d89986..479d7902aa111 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -2697,6 +2697,19 @@ def test_frame_ctor_datetime64_column(self):
         df = DataFrame({"A": np.random.randn(len(rng)), "B": dates})
         assert np.issubdtype(df["B"].dtype, np.dtype("M8[ns]"))
 
+    def test_dataframe_constructor_infer_multiindex(self):
+        index_lists = [["a", "a", "b", "b"], ["x", "y", "x", "y"]]
+
+        multi = DataFrame(
+            np.random.randn(4, 4),
+            index=[np.array(x) for x in index_lists],
+        )
+        assert isinstance(multi.index, MultiIndex)
+        assert not isinstance(multi.columns, MultiIndex)
+
+        multi = DataFrame(np.random.randn(4, 4), columns=index_lists)
+        assert isinstance(multi.columns, MultiIndex)
+
     @pytest.mark.parametrize(
         "input_vals",
         [
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index ec8a690e6e7f9..adbdf1077113e 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -1536,6 +1536,18 @@ def test_series_constructor_datetimelike_index_coercion(self):
             assert ser.index.is_all_dates
         assert isinstance(ser.index, DatetimeIndex)
 
+    def test_series_constructor_infer_multiindex(self):
+        index_lists = [["a", "a", "b", "b"], ["x", "y", "x", "y"]]
+
+        multi = Series(1.0, index=[np.array(x) for x in index_lists])
+        assert isinstance(multi.index, MultiIndex)
+
+        multi = Series(1.0, index=index_lists)
+        assert isinstance(multi.index, MultiIndex)
+
+        multi = Series(range(4), index=index_lists)
+        assert isinstance(multi.index, MultiIndex)
+
 
 class TestSeriesConstructorInternals:
     def test_constructor_no_pandas_array(self):
diff --git a/pandas/tests/test_multilevel.py b/pandas/tests/test_multilevel.py
index 901049209bf64..6f5345f802a7c 100644
--- a/pandas/tests/test_multilevel.py
+++ b/pandas/tests/test_multilevel.py
@@ -21,42 +21,6 @@
 
 
 class TestMultiLevel:
-    def test_append(self, multiindex_dataframe_random_data):
-        frame = multiindex_dataframe_random_data
-
-        a, b = frame[:5], frame[5:]
-
-        result = a.append(b)
-        tm.assert_frame_equal(result, frame)
-
-        result = a["A"].append(b["A"])
-        tm.assert_series_equal(result, frame["A"])
-
-    def test_dataframe_constructor_infer_multiindex(self):
-        multi = DataFrame(
-            np.random.randn(4, 4),
-            index=[np.array(["a", "a", "b", "b"]), np.array(["x", "y", "x", "y"])],
-        )
-        assert isinstance(multi.index, MultiIndex)
-        assert not isinstance(multi.columns, MultiIndex)
-
-        multi = DataFrame(
-            np.random.randn(4, 4), columns=[["a", "a", "b", "b"], ["x", "y", "x", "y"]]
-        )
-        assert isinstance(multi.columns, MultiIndex)
-
-    def test_series_constructor_infer_multiindex(self):
-        multi = Series(
-            1.0, index=[np.array(["a", "a", "b", "b"]), np.array(["x", "y", "x", "y"])]
-        )
-        assert isinstance(multi.index, MultiIndex)
-
-        multi = Series(1.0, index=[["a", "a", "b", "b"], ["x", "y", "x", "y"]])
-        assert isinstance(multi.index, MultiIndex)
-
-        multi = Series(range(4), index=[["a", "a", "b", "b"], ["x", "y", "x", "y"]])
-        assert isinstance(multi.index, MultiIndex)
-
     def test_reindex_level(self, multiindex_year_month_day_dataframe_random_data):
         # axis=0
         ymd = multiindex_year_month_day_dataframe_random_data
@@ -278,18 +242,17 @@ def test_std_var_pass_ddof(self):
             expected = df.groupby(level=0).agg(alt)
             tm.assert_frame_equal(result, expected)
 
-    def test_frame_series_agg_multiple_levels(
-        self, multiindex_year_month_day_dataframe_random_data
+    @pytest.mark.parametrize("klass", [Series, DataFrame])
+    def test_agg_multiple_levels(
+        self, multiindex_year_month_day_dataframe_random_data, klass
     ):
         ymd = multiindex_year_month_day_dataframe_random_data
+        if klass is Series:
+            ymd = ymd["A"]
 
         result = ymd.sum(level=["year", "month"])
         expected = ymd.groupby(level=["year", "month"]).sum()
-        tm.assert_frame_equal(result, expected)
-
-        result = ymd["A"].sum(level=["year", "month"])
-        expected = ymd["A"].groupby(level=["year", "month"]).sum()
-        tm.assert_series_equal(result, expected)
+        tm.assert_equal(result, expected)
 
     def test_groupby_multilevel(self, multiindex_year_month_day_dataframe_random_data):
         ymd = multiindex_year_month_day_dataframe_random_data