diff --git a/ci/code_checks.sh b/ci/code_checks.sh
index af1d93d1f153b..4d3ebe393c262 100755
--- a/ci/code_checks.sh
+++ b/ci/code_checks.sh
@@ -70,7 +70,6 @@ if [[ -z "$CHECK" || "$CHECK" == "docstrings" ]]; then
         --format=actions \
         -i ES01 `# For now it is ok if docstrings are missing the extended summary` \
         -i "pandas.Series.dt PR01" `# Accessors are implemented as classes, but we do not document the Parameters section` \
-        -i "pandas.MultiIndex.copy PR07,RT03,SA01" \
         -i "pandas.MultiIndex.get_level_values SA01" \
         -i "pandas.MultiIndex.get_loc PR07" \
         -i "pandas.MultiIndex.get_loc_level PR07" \
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index c278927c1db6e..ee271cc7be86c 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1282,20 +1282,37 @@ def copy(  # type: ignore[override]
         name=None,
     ) -> Self:
         """
-        Make a copy of this object.
+        Make a copy of this object. Names, dtype, levels and codes can be passed and \
+        will be set on new copy.
 
-        Names, dtype, levels and codes can be passed and will be set on new copy.
+        The `copy` method provides a mechanism to create a duplicate of an
+        existing MultiIndex object. This is particularly useful in scenarios where
+        modifications are required on an index, but the original MultiIndex should
+        remain unchanged. By specifying the `deep` parameter, users can control
+        whether the copy should be a deep or shallow copy, providing flexibility
+        depending on the size and complexity of the MultiIndex.
 
         Parameters
         ----------
         names : sequence, optional
+            Names to set on the new MultiIndex object.
         deep : bool, default False
+            If False, the new object will be a shallow copy. If True, a deep copy
+            will be attempted. Deep copying can be potentially expensive for large
+            MultiIndex objects.
         name : Label
             Kept for compatibility with 1-dimensional Index. Should not be used.
 
         Returns
         -------
         MultiIndex
+            A new MultiIndex object with the specified modifications.
+
+        See Also
+        --------
+        MultiIndex.from_arrays : Convert arrays to MultiIndex.
+        MultiIndex.from_tuples : Convert list of tuples to MultiIndex.
+        MultiIndex.from_frame : Convert DataFrame to MultiIndex.
 
         Notes
         -----