diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 4de95079f6480..69d53b04cf9f6 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5167,6 +5167,7 @@ def set_value(self, arr, key, value):
     def get_indexer_non_unique(self, target) -> tuple[np.ndarray, np.ndarray]:
         # both returned ndarrays are np.intp
         target = ensure_index(target)
+        target = self._maybe_cast_listlike_indexer(target)
 
         if not self._should_compare(target) and not is_interval_dtype(self.dtype):
             # IntervalIndex get special treatment bc numeric scalars can be
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 1bda05f3ce5df..2ebc39664ad60 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -12,17 +12,12 @@
 
 from pandas._libs import index as libindex
 from pandas._typing import (
-    ArrayLike,
     Dtype,
     DtypeObj,
 )
-from pandas.util._decorators import (
-    Appender,
-    doc,
-)
+from pandas.util._decorators import doc
 
 from pandas.core.dtypes.common import (
-    ensure_platform_int,
     is_categorical_dtype,
     is_scalar,
 )
@@ -41,7 +36,6 @@
 import pandas.core.indexes.base as ibase
 from pandas.core.indexes.base import (
     Index,
-    _index_shared_docs,
     maybe_extract_name,
 )
 from pandas.core.indexes.extension import (
@@ -492,38 +486,9 @@ def _maybe_cast_indexer(self, key) -> int:
                 return -1
             raise
 
-    def _get_indexer(
-        self,
-        target: Index,
-        method: str | None = None,
-        limit: int | None = None,
-        tolerance=None,
-    ) -> np.ndarray:
-        # returned ndarray is np.intp
-
-        if self.equals(target):
-            return np.arange(len(self), dtype="intp")
-
-        return self._get_indexer_non_unique(target._values)[0]
-
-    @Appender(_index_shared_docs["get_indexer_non_unique"] % _index_doc_kwargs)
-    def get_indexer_non_unique(self, target) -> tuple[np.ndarray, np.ndarray]:
-        # both returned ndarrays are np.intp
-        target = ibase.ensure_index(target)
-        return self._get_indexer_non_unique(target._values)
-
-    def _get_indexer_non_unique(
-        self, values: ArrayLike
-    ) -> tuple[np.ndarray, np.ndarray]:
-        # both returned ndarrays are np.intp
-        """
-        get_indexer_non_unique but after unrapping the target Index object.
-        """
-        # Note: we use engine.get_indexer_non_unique for get_indexer in addition
-        #  to get_indexer_non_unique because, even if `target` is unique, any
-        #  non-category entries in it will be encoded as -1  so `codes` may
-        #  not be unique.
-
+    def _maybe_cast_listlike_indexer(self, values) -> CategoricalIndex:
+        if isinstance(values, CategoricalIndex):
+            values = values._data
         if isinstance(values, Categorical):
             # Indexing on codes is more efficient if categories are the same,
             #  so we can apply some optimizations based on the degree of
@@ -532,9 +497,9 @@ def _get_indexer_non_unique(
             codes = cat._codes
         else:
             codes = self.categories.get_indexer(values)
-
-        indexer, missing = self._engine.get_indexer_non_unique(codes)
-        return ensure_platform_int(indexer), ensure_platform_int(missing)
+            codes = codes.astype(self.codes.dtype, copy=False)
+            cat = self._data._from_backing_data(codes)
+        return type(self)._simple_new(cat)
 
     # --------------------------------------------------------------------
 
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index df7fae0763c42..aeef37dfb9af6 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -45,6 +45,7 @@
 
 from pandas.core.arrays import (
     DatetimeArray,
+    ExtensionArray,
     PeriodArray,
     TimedeltaArray,
 )
@@ -595,7 +596,12 @@ def _maybe_cast_listlike_indexer(self, keyarr):
         try:
             res = self._data._validate_listlike(keyarr, allow_object=True)
         except (ValueError, TypeError):
-            res = com.asarray_tuplesafe(keyarr)
+            if not isinstance(keyarr, ExtensionArray):
+                # e.g. we don't want to cast DTA to ndarray[object]
+                res = com.asarray_tuplesafe(keyarr)
+                # TODO: com.asarray_tuplesafe shouldn't cast e.g. DatetimeArray
+            else:
+                res = keyarr
         return Index(res, dtype=res.dtype)