PERF: tighten _should_compare for MultiIndex

pandas/core/indexes/base.py

@@ -5345,6 +5345,16 @@ def _get_indexer_non_comparable(
         """
         if method is not None:
             other = unpack_nested_dtype(target)
+            if self._is_multi ^ other._is_multi:
+                kind = other.dtype.type if self._is_multi else self.dtype.type
+                raise TypeError(
+                    f"'<' not supported between instances of {kind} and 'tuple'"
+                )
+            elif self._is_multi and other._is_multi:
+                assert self.nlevels != other.nlevels
+                # Python allows comparison between tuples of different lengths,
+                #  but for our purposes such a comparison is not meaningful.
+                raise TypeError("'<' not supported between tuples of different lengths")
             raise TypeError(f"Cannot compare dtypes {self.dtype} and {other.dtype}")
 
         no_matches = -1 * np.ones(target.shape, dtype=np.intp)
@@ -5474,6 +5484,14 @@ def _should_compare(self, other: Index) -> bool:
 
         other = unpack_nested_dtype(other)
         dtype = other.dtype
+        if other._is_multi:
+            if not self._is_multi:
+                # other contains only tuples so unless we are object-dtype,
+                #  there can never be any matches
+                return self._is_comparable_dtype(dtype)
+            return self.nlevels == other.nlevels
+            # TODO: we can get more specific requiring levels are comparable?
+
         return self._is_comparable_dtype(dtype) or is_object_dtype(dtype)
 
     def _is_comparable_dtype(self, dtype: DtypeObj) -> bool:

pandas/tests/indexes/multi/test_indexing.py

@@ -457,6 +457,15 @@ def test_get_indexer_kwarg_validation(self):
         with pytest.raises(ValueError, match=msg):
             mi.get_indexer(mi[:-1], tolerance="piano")
 
+    def test_get_indexer_mismatched_nlevels(self):
+        mi = MultiIndex.from_product([range(3), ["A", "B"]])
+
+        other = MultiIndex.from_product([range(3), ["A", "B"], range(2)])
+
+        msg = "tuples of different lengths"
+        with pytest.raises(TypeError, match=msg):
+            mi.get_indexer(other, method="pad")
+
 
 def test_getitem(idx):
     # scalar