diff --git a/pandas/core/base.py b/pandas/core/base.py
index d831dc69338bd..26fea89b45ae1 100644
--- a/pandas/core/base.py
+++ b/pandas/core/base.py
@@ -663,6 +663,21 @@ def transpose(self, *args, **kwargs):
     T = property(transpose, doc="return the transpose, which is by "
                                 "definition self")
 
+    @property
+    def _is_homogeneous(self):
+        """Whether the object has a single dtype.
+
+        By definition, Series and Index are always considered homogeneous.
+        A MultiIndex may or may not be homogeneous, depending on the
+        dtypes of the levels.
+
+        See Also
+        --------
+        DataFrame._is_homogeneous
+        MultiIndex._is_homogeneous
+        """
+        return True
+
     @property
     def shape(self):
         """ return a tuple of the shape of the underlying data """
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index bb221ced9e6bd..959b0a4fd1890 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -613,6 +613,34 @@ def shape(self):
         """
         return len(self.index), len(self.columns)
 
+    @property
+    def _is_homogeneous(self):
+        """
+        Whether all the columns in a DataFrame have the same type.
+
+        Returns
+        -------
+        bool
+
+        Examples
+        --------
+        >>> DataFrame({"A": [1, 2], "B": [3, 4]})._is_homogeneous
+        True
+        >>> DataFrame({"A": [1, 2], "B": [3.0, 4.0]})._is_homogeneous
+        False
+
+        Items with the same type but different sizes are considered
+        different types.
+
+        >>> DataFrame({"A": np.array([1, 2], dtype=np.int32),
+        ...            "B": np.array([1, 2], dtype=np.int64)})._is_homogeneous
+        False
+        """
+        if self._data.any_extension_types:
+            return len({block.dtype for block in self._data.blocks}) == 1
+        else:
+            return not self._data.is_mixed_type
+
     def _repr_fits_vertical_(self):
         """
         Check length against max_rows.
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index a7932f667f6de..ad38f037b6578 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -288,6 +288,26 @@ def _verify_integrity(self, labels=None, levels=None):
     def levels(self):
         return self._levels
 
+    @property
+    def _is_homogeneous(self):
+        """Whether the levels of a MultiIndex all have the same dtype.
+
+        This looks at the dtypes of the levels.
+
+        See Also
+        --------
+        Index._is_homogeneous
+        DataFrame._is_homogeneous
+
+        Examples
+        --------
+        >>> MultiIndex.from_tuples([('a', 'b'), ('a', 'c')])._is_homogeneous
+        True
+        >>> MultiIndex.from_tuples([('a', 1), ('a', 2)])._is_homogeneous
+        False
+        """
+        return len({x.dtype for x in self.levels}) <= 1
+
     def _set_levels(self, levels, level=None, copy=False, validate=True,
                     verify_integrity=False):
         # This is NOT part of the levels property because it should be
diff --git a/pandas/tests/frame/test_dtypes.py b/pandas/tests/frame/test_dtypes.py
index 3b3ab3d03dce9..ca4bd64659e06 100644
--- a/pandas/tests/frame/test_dtypes.py
+++ b/pandas/tests/frame/test_dtypes.py
@@ -815,6 +815,30 @@ def test_constructor_list_str_na(self, string_dtype):
         expected = DataFrame({"A": ['1.0', '2.0', None]}, dtype=object)
         assert_frame_equal(result, expected)
 
+    @pytest.mark.parametrize("data, expected", [
+        # empty
+        (DataFrame(), True),
+        # multi-same
+        (DataFrame({"A": [1, 2], "B": [1, 2]}), True),
+        # multi-object
+        (DataFrame({"A": np.array([1, 2], dtype=object),
+                    "B": np.array(["a", "b"], dtype=object)}), True),
+        # multi-extension
+        (DataFrame({"A": pd.Categorical(['a', 'b']),
+                    "B": pd.Categorical(['a', 'b'])}), True),
+        # differ types
+        (DataFrame({"A": [1, 2], "B": [1., 2.]}), False),
+        # differ sizes
+        (DataFrame({"A": np.array([1, 2], dtype=np.int32),
+                    "B": np.array([1, 2], dtype=np.int64)}), False),
+        # multi-extension differ
+        (DataFrame({"A": pd.Categorical(['a', 'b']),
+                    "B": pd.Categorical(['b', 'c'])}), False),
+
+    ])
+    def test_is_homogeneous(self, data, expected):
+        assert data._is_homogeneous is expected
+
 
 class TestDataFrameDatetimeWithTZ(TestData):
 
diff --git a/pandas/tests/indexing/test_multiindex.py b/pandas/tests/indexing/test_multiindex.py
index 9e66dfad3ddc7..aefa8badf72e7 100644
--- a/pandas/tests/indexing/test_multiindex.py
+++ b/pandas/tests/indexing/test_multiindex.py
@@ -733,6 +733,14 @@ def test_multiindex_contains_dropped(self):
         assert 'a' in idx.levels[0]
         assert 'a' not in idx
 
+    @pytest.mark.parametrize("data, expected", [
+        (MultiIndex.from_product([(), ()]), True),
+        (MultiIndex.from_product([(1, 2), (3, 4)]), True),
+        (MultiIndex.from_product([('a', 'b'), (1, 2)]), False),
+    ])
+    def test_multiindex_is_homogeneous(self, data, expected):
+        assert data._is_homogeneous is expected
+
 
 class TestMultiIndexSlicers(object):
 
diff --git a/pandas/tests/series/test_dtypes.py b/pandas/tests/series/test_dtypes.py
index 7aecaf340a3e0..83a458eedbd93 100644
--- a/pandas/tests/series/test_dtypes.py
+++ b/pandas/tests/series/test_dtypes.py
@@ -508,3 +508,8 @@ def test_infer_objects_series(self):
 
         assert actual.dtype == 'object'
         tm.assert_series_equal(actual, expected)
+
+    def test_is_homogeneous(self):
+        assert Series()._is_homogeneous
+        assert Series([1, 2])._is_homogeneous
+        assert Series(pd.Categorical([1, 2]))._is_homogeneous