Like minkhollow says, I mostly did this with Ray, and at first it was just to play with continuities. Ray is from a Ghostbusters comic book miniseries from 2003, which was set in 2003- but everything in the movie happened in 2003ish rather than 1984ish. I've thrown Ray into the movieverse proper, into the Real Ghostbusters cartoon, into an AU where the Men in Black organization existed and basically swooped down on him about a day and a half after his parents died, into another AU where Columbia never cut the guys' funding so they never formed the Ghostbusters but the Shandor Building was busily summoning Gozer anyway... possibly one or two others, too, but I don't entirely recall just at the moment. One constant was that Ray could not be present in the same universe as one of his alternates at the same time, or one or the other of them would be punted out to Milliways.