Here's my take:
Its 30 Years after the events in Ghostbusters II:
A group of ghostbusters (not the original cast) comes shuffling in to a rundown building with the "no ghost" sign flickering in disrepair. The facility is run down, dirty and sad.
Dirty, tired and slimed. Each of them is toting several smoking traps.
We find out that Ghostbusters has turned into a franchise paranormal extermination business. Branches in a few places, all of which have failed.
This is the last one. (NYC old firehouse location maybe?)
Paranormal activity is on the rise. Somethings up NYC, there getting their asses kicked. A corrupted former mayor of NYC (ghost) was also a Gozer worshiper. Is trying to get resurrected so he can come back and rule NYC. Their equipment is failing, overheating, etc. They've run out of money and resources.
They try to get in touch with the owners of the franchise, cause none of this crap is in the 'Buster manual.
Winston is the only one they can reach at first, he owns a chain of restaurants in New York.
After a paranormal confrontation he agrees to help contact the old gang.
Peter is on an Island in the Caribbean. He's fabulously wealthy, having married the only daughter of a Mideastern Oil Sheik. Doesn't want to get involved, but is willing to write a check and come to the after party.
Egon has passed away while hunting Fungi in the Amazon. We find out he has a daughter that attends MIT.
Ray is running a Summer Camp in Minnesota for kids who are paranormally gifted.
None of the old gang is willing to get directly involved, but Ray suggests he introduces them to Egon's daughter.
better writers would have to take it from here