I've broken a taboo and created a Star Wars (and its even better Spaceballs parody) and a Star Trek TNG / DS9 (as well as 2020s real online / offline life) crossover: Queen Padmé Tales. The story so far: slashdot.org's darling Israeli-American filmmaker Natalie Portman has realised that Hollywood's disapproval of crossovers / parodies / etc and its insistence of accepting only screenplays in its draconian, finnicky, and boring format has deprived it of almost all honest hobbyist screenplay writers and made most big name "acting-for-fun" actors "unemployed".
As a result, she licensed some franchises (not that a big studio will dare sue her because its share value will plumet) and decided to direct or codirect the 1992-born YouTube pop singer and budding actress Tiffany Alvord as Portman's iconic Queen Padmé Amidala, due to Alvord having better Internet-savviness.
Queen Padmé is 10 years into her reign, and needs to handle a range of issues, such as the first attempt to assassinate her (by two Klingon warriors), and fighting global warming in Planet Spaceball.
Best of all in a true open-content fashion, the screenplays' sources (and the franchise) are under CC-by and in a GitHub repo and I encourage contributors to fork it, take it into their own direction, send merge requests, or even convert it to a different licence. I still reserve the right to reject merging changes that I disapprove of, but you can always keep them under your own branch.