If Ghostbusters III is to be successfull I think that it must have the tone of the first movie, the very best SFX in the business and above all a very well written and original script.
I think that any sequel, no matter what the francise, should go in a new direction while keeping the ingredients fans recognise and love for the francise in question. Otherwise the movie is predictable and uninteresting. It is very easy to repeat yourself which is of course unfortunately what happens so often in Hollywood. This is of course exactly what happened with Ghostbusters II, which I think did more harm than good to the francise.
However, I do understand the difficulty in writing a good sequel to Ghostbusters because there is only so much you can do with it. What I mean by that is that script ideas are far more limited when comparing writing a script for, lets say a new James Bond picture because with James Bond the sky is the limit with story, characters, locations etc but at the same time, as I said before, each one of those films has those recognisable ingredients that you would associate with a Bond movie.
Personally I wouldn't mind if Dan Aykroyd and Harold Ramis gave the script writing job to someone else as long as it turns out to be well written and original.