We had something like this back before the TG subforum came into being, but a search didn’t find it…
Anyway, the previous person, after penning their riff, puts in a legitimate non-porn movie title-and the next person then corrupts or perverts it (then puts in another legitimate title for the next person). Hilarity ensues.
e.g.
Saving Private Ryan
[becomes]
Shaving Ryan’s Privates
So, away we go!
The Bridge on the River Kwai