Well, you can use this same "motif" approach with retelling any story, although it works best with a really LONG story (or an epic) so that you have lots and lots of motifs to choose from!
Just ignore the plot completely and pull out the raw ingredients, the "motifs" or basic elements of the story, and use them to create your own story. Try to pick 5 (or more) motifs from the original source story so that your readers will be able to see the connection. These can be types of characters that appear in your source story (princess, witch, dog, etc.), objects that appear in the source story (golden ring, magic lamp, poison, etc.), and elements of the setting in the source story (swamp, palace, desert, etc.). Then, make up your own plot using those raw ingredients, and explain in your note just which elements in your story came from your source.