You know, I wouldn't have mind a continuation with only two of the Ghostbusters coming back (especially if Bill Murry is completely opposed to it and since Harold Ramis passed away). Extreme Ghostbusters did it with having Egon being in charge of a younger group. What's not the say that they couldn't do the same with the film? Have Winston move up as being the man in charge of the Ghostbusters HQ while Ray works on the equipment and teachers the young Ghostbusters how to do the job (even doing performance reviews with the members in hopes to improve their skills and abilities at becoming excellent Ghostbusters). They could have it explain that Peter has made millions on the franchise rights and has completely retired and Egon passed away years ago (but they have a dedication plaque for him at the entrance to the HQ. And Janine could still be there, still complaining about the poor amount of pay for answering phones (or, they could have her and Lewis married and relocated to a small suburbs out of the city). I even imagined that one of the younger Ghostbusters be Oscar from the second film, now all grown up and being a Ghostbuster against Dana's wishes.
And, of course, being someone who has done fan fiction, I actually came up with an idea for a story for the third film, which would have involved the time travel aspect that had been originally created by Dan Aykroyd for the original version of the film (basically, having some sort of experiment going on at the GBHQ and something in the past is changed, completely wiping out all of mankind after a certain date, but the experiment leaving the HQ and those within it still intact. The Ghostbusters have to go through these doorways in time to end up in certain time periods, leaving them to capture certain ghosts and stop whatever demonic creature from succeeding in its plan on wiping out humanity, in hopes that they can restore the timeline back to how it was. (Yeah, I know, it sounds lame).