I had a go at trying to come up with a premise last year for how I would do a third movie. Essentially, the idea was that, by the end of the 90s, Ghostbusters Inc had headquarters in NYC, LA, and Chicago, to hit the hubs of paranormal activity in the country, with smaller field offices in DC, Miami, Dallas, and Seattle. By the end of the 2000's the combination of a decade of trapping and economic downturn forced all of them to close, except the NYC HQ, which is left downsized to a skeleton crew. Have Stantz still in charge, but the others have moved on. This would allow for new characters to already be a part of the team, maybe with some involvement still from Winston.
I played around with different character types to have on the team, to fill some of the narrative roles of the original members without necessarily retreading old beats. One that I landed on that I particularly liked was the idea of having a Ghostbuster who went through seminary, but left before coming a priest. I've always joked that Catholics are like God's SWAT team, so I felt like having someone from that world would bring an interesting dynamic to the character roster.