REF: avoid need for get_join_target in join_non_unique

pandas/core/indexes/base.py

@@ -4092,8 +4092,6 @@ def join(
         join_index, (left_indexer, right_indexer)
         """
         other = ensure_index(other)
-        self_is_mi = isinstance(self, ABCMultiIndex)
-        other_is_mi = isinstance(other, ABCMultiIndex)
 
         if isinstance(self, ABCDatetimeIndex) and isinstance(other, ABCDatetimeIndex):
             if (self.tz is None) ^ (other.tz is None):
@@ -4113,7 +4111,7 @@ def join(
 
         # try to figure out the join level
         # GH3662
-        if level is None and (self_is_mi or other_is_mi):
+        if level is None and (self._is_multi or other._is_multi):
 
             # have the same levels/names so a simple join
             if self.names == other.names:
@@ -4122,7 +4120,7 @@ def join(
                 return self._join_multi(other, how=how)
 
         # join on the level
-        if level is not None and (self_is_mi or other_is_mi):
+        if level is not None and (self._is_multi or other._is_multi):
             return self._join_level(other, level, how=how)
 
         if len(other) == 0 and how in ("left", "outer"):
@@ -4171,8 +4169,20 @@ def join(
             try:
                 return self._join_monotonic(other, how=how)
             except TypeError:
+                # object dtype; non-comparable objects
                 pass
 
+        return self._join_via_get_indexer(other, how, sort)
+
+    @final
+    def _join_via_get_indexer(
+        self, other: Index, how: str_t, sort: bool
+    ) -> tuple[Index, npt.NDArray[np.intp] | None, npt.NDArray[np.intp] | None]:
+        # Fallback if we do not have any fastpaths available based on
+        #  uniqueness/monotonicity
+
+        # Note: at this point we have checked matching dtypes
+
         if how == "left":
             join_index = self
         elif how == "right":
@@ -4282,22 +4292,25 @@ def _join_non_unique(
         # We only get here if dtypes match
         assert self.dtype == other.dtype
 
-        lvalues = self._get_join_target()
-        rvalues = other._get_join_target()
-
         left_idx, right_idx = get_join_indexers(
-            [lvalues], [rvalues], how=how, sort=True
+            [self._values], [other._values], how=how, sort=True
         )
+        mask = left_idx == -1
 
-        left_idx = ensure_platform_int(left_idx)
-        right_idx = ensure_platform_int(right_idx)
+        # error: Argument 1 to "take" of "ExtensionArray" has incompatible
+        # type "ndarray[Any, dtype[signedinteger[Any]]]"; expected "Sequence[int]"
+        join_array = self._values.take(left_idx)  # type: ignore[arg-type]
+        # error: Argument 1 to "take" of "ExtensionArray" has incompatible type
+        # "ndarray[Any, dtype[signedinteger[Any]]]"; expected "Sequence[int]"
+        right = other._values.take(right_idx)  # type: ignore[arg-type]
 
-        join_array = np.asarray(lvalues.take(left_idx))
-        mask = left_idx == -1
-        np.putmask(join_array, mask, rvalues.take(right_idx))
+        if isinstance(join_array, np.ndarray):
+            np.putmask(join_array, mask, right)
+        else:
+            # error: "ExtensionArray" has no attribute "putmask"
+            join_array.putmask(mask, right)  # type: ignore[attr-defined]
 
-        join_arraylike = self._from_join_target(join_array)
-        join_index = self._wrap_joined_index(join_arraylike, other)
+        join_index = self._wrap_joined_index(join_array, other)
 
         return join_index, left_idx, right_idx
 
@@ -4450,7 +4463,9 @@ def _get_leaf_sorter(labels: list[np.ndarray]) -> npt.NDArray[np.intp]:
         return join_index, left_indexer, right_indexer
 
     @final
-    def _join_monotonic(self, other: Index, how: str_t = "left"):
+    def _join_monotonic(
+        self, other: Index, how: str_t = "left"
+    ) -> tuple[Index, npt.NDArray[np.intp] | None, npt.NDArray[np.intp] | None]:
         # We only get here with matching dtypes
         assert other.dtype == self.dtype