I saw a lot of confusion on the distiction between parody (generally okay, relatively easier defense) and satire (sometimes okay, relatively harder defense) in the Psy and Copyright discussion thread. I've found this document from an American Bar Association roundtable quite informative for exploring the distinction.

Of course, nothing is cut and dry here, and you'll always want to weigh how much you want to risk having to pay for legal representation vs. how much you want to produce this new work.