Can't combine DatetimeIndex MultiIndex with numeric MultiIndex

pandas/tests/reshape/concat/test_index.py

@@ -257,3 +257,52 @@ def test_concat_multiindex_dfs_with_deepcopy(self):
         tm.assert_frame_equal(result_copy, expected)
         result_no_copy = concat(example_dict, names=["testname"])
         tm.assert_frame_equal(result_no_copy, expected)
+
+    @pytest.mark.parametrize(
+        "mi1_list",
+        [
+            [["a"], range(2)],
+            [["b"], np.arange(2.0, 4.0)],
+            [["c"], ["A", "B"]],
+            [["d"], pd.date_range(start="2017", end="2018", periods=2)],
+        ],
+    )
+    @pytest.mark.parametrize(
+        "mi2_list",
+        [
+            [["a"], range(2)],
+            [["b"], np.arange(2.0, 4.0)],
+            [["c"], ["A", "B"]],
+            [["d"], pd.date_range(start="2017", end="2018", periods=2)],
+        ],
+    )
+    def test_concat_with_various_multiindex_dtypes(
+        self, mi1_list: list, mi2_list: list
+    ):
+        # GitHub #23478
+        mi1 = MultiIndex.from_product(mi1_list)
+        mi2 = MultiIndex.from_product(mi2_list)
+
+        df1 = DataFrame(np.zeros((1, len(mi1))), columns=mi1)
+        df2 = DataFrame(np.zeros((1, len(mi2))), columns=mi2)
+
+        if mi1_list[0] == mi2_list[0]:
+            expected_mi = MultiIndex(
+                levels=[mi1_list[0], list(mi1_list[1])],
+                codes=[[0, 0, 0, 0], [0, 1, 0, 1]],
+            )
+        else:
+            expected_mi = MultiIndex(
+                levels=[
+                    mi1_list[0] + mi2_list[0],
+                    list(mi1_list[1]) + list(mi2_list[1]),
+                ],
+                codes=[[0, 0, 1, 1], [0, 1, 2, 3]],
+            )
+
+        expected_df = DataFrame(np.zeros((1, len(expected_mi))), columns=expected_mi)
+
+        with tm.assert_produces_warning(None):
+            result_df = concat((df1, df2), axis=1)
+
+        tm.assert_frame_equal(expected_df, result_df)