diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index 18506b871bda6..b2041a3e1380a 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -266,7 +266,11 @@ def aggregate(self, func=None, *args, engine=None, engine_kwargs=None, **kwargs)
             func = maybe_mangle_lambdas(func)
             ret = self._aggregate_multiple_funcs(func)
             if relabeling:
-                ret.columns = columns
+                # error: Incompatible types in assignment (expression has type
+                # "Optional[List[str]]", variable has type "Index")
+                ret.columns = columns  # type: ignore[assignment]
+            return ret
+
         else:
             cyfunc = com.get_cython_func(func)
             if cyfunc and not args and not kwargs:
@@ -282,33 +286,21 @@ def aggregate(self, func=None, *args, engine=None, engine_kwargs=None, **kwargs)
                 #  see test_groupby.test_basic
                 result = self._aggregate_named(func, *args, **kwargs)
 
-            index = Index(sorted(result), name=self.grouper.names[0])
-            ret = create_series_with_explicit_dtype(
-                result, index=index, dtype_if_empty=object
-            )
-
-        if not self.as_index:  # pragma: no cover
-            print("Warning, ignoring as_index=True")
-
-        if isinstance(ret, dict):
-            from pandas import concat
-
-            ret = concat(ret.values(), axis=1, keys=[key.label for key in ret.keys()])
-        return ret
+                index = Index(sorted(result), name=self.grouper.names[0])
+                return create_series_with_explicit_dtype(
+                    result, index=index, dtype_if_empty=object
+                )
 
     agg = aggregate
 
-    def _aggregate_multiple_funcs(self, arg):
+    def _aggregate_multiple_funcs(self, arg) -> DataFrame:
         if isinstance(arg, dict):
 
             # show the deprecation, but only if we
             # have not shown a higher level one
             # GH 15931
-            if isinstance(self._selected_obj, Series):
-                raise SpecificationError("nested renamer is not supported")
+            raise SpecificationError("nested renamer is not supported")
 
-            columns = list(arg.keys())
-            arg = arg.items()
         elif any(isinstance(x, (tuple, list)) for x in arg):
             arg = [(x, x) if not isinstance(x, (tuple, list)) else x for x in arg]
 
@@ -335,8 +327,14 @@ def _aggregate_multiple_funcs(self, arg):
             results[base.OutputKey(label=name, position=idx)] = obj.aggregate(func)
 
         if any(isinstance(x, DataFrame) for x in results.values()):
-            # let higher level handle
-            return results
+            from pandas import concat
+
+            res_df = concat(
+                results.values(), axis=1, keys=[key.label for key in results.keys()]
+            )
+            # error: Incompatible return value type (got "Union[DataFrame, Series]",
+            # expected "DataFrame")
+            return res_df  # type: ignore[return-value]
 
         indexed_output = {key.position: val for key, val in results.items()}
         output = self.obj._constructor_expanddim(indexed_output, index=None)
@@ -1000,6 +998,11 @@ def aggregate(self, func=None, *args, engine=None, engine_kwargs=None, **kwargs)
         result = op.agg()
         if not is_dict_like(func) and result is not None:
             return result
+        elif relabeling and result is not None:
+            # this should be the only (non-raising) case with relabeling
+            # used reordered index of columns
+            result = result.iloc[:, order]
+            result.columns = columns
 
         if result is None:
 
@@ -1039,12 +1042,6 @@ def aggregate(self, func=None, *args, engine=None, engine_kwargs=None, **kwargs)
                             [sobj.columns.name] * result.columns.nlevels
                         ).droplevel(-1)
 
-        if relabeling:
-
-            # used reordered index of columns
-            result = result.iloc[:, order]
-            result.columns = columns
-
         if not self.as_index:
             self._insert_inaxis_grouper_inplace(result)
             result.index = np.arange(len(result))
@@ -1389,9 +1386,7 @@ def _transform_item_by_item(self, obj: DataFrame, wrapper) -> DataFrame:
         if not output:
             raise TypeError("Transform function invalid for data types")
 
-        columns = obj.columns
-        if len(output) < len(obj.columns):
-            columns = columns.take(inds)
+        columns = obj.columns.take(inds)
 
         return self.obj._constructor(output, index=obj.index, columns=columns)
 
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index c5ef18c51a533..d222bc1c083ed 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -2174,7 +2174,9 @@ def backfill(self, limit=None):
     @final
     @Substitution(name="groupby")
     @Substitution(see_also=_common_see_also)
-    def nth(self, n: int | list[int], dropna: str | None = None) -> DataFrame:
+    def nth(
+        self, n: int | list[int], dropna: Literal["any", "all", None] = None
+    ) -> DataFrame:
         """
         Take the nth row from each group if n is an int, or a subset of rows
         if n is a list of ints.
@@ -2187,9 +2189,9 @@ def nth(self, n: int | list[int], dropna: str | None = None) -> DataFrame:
         ----------
         n : int or list of ints
             A single nth value for the row or a list of nth values.
-        dropna : None or str, optional
+        dropna : {'any', 'all', None}, default None
             Apply the specified dropna operation before counting which row is
-            the nth row. Needs to be None, 'any' or 'all'.
+            the nth row.
 
         Returns
         -------