I think that, realistically, it's getting to this point:
No GBIII. Done. Over.
However, I don't think the franchise is done.
The movies were such a HUGE hit that the franchise has potential. I'm not saying I like it, but I could EASILY see a Ghostbusters remake in another 10 years or so.
Then, they restart the franchise completely. Probably a different version of Ghostbusters II. Then maybe, just maybe, a Ghostbusters III, but nowhere near the way most of us want to see it now.
Hollywood loves to do remakes. With so many complicated issues holding a sequel back, it is totally likely that the studio is just waiting to restart the franchise fresh. I hope this isn't considered blasphemy, but I think it could work. I would hope and pray for nearly a shot for shot remake of the original (that's probably not that realistic, but come on, the premise works so darn well that not much would need to be changed).
Just a thought.