Story-wise, they could tie up some loose ends, such as the missing agent Desmond. The way S3 ended left a clear open possibility of Richard and Carrie continuing their pursuit of a way out or back, but that then would be an expectation, and we've seen what S3 did to expectations. And here is why I am at this point more inclined to think that S4 is more unlikely that not: with Dougie Jones' return Cooper's story ends, it is a closure. Cooper lives on as "corrected" Dougie Jones, having a proper family of his own. What about Richard's fate? Would a new season be warranted to rectify it? At this moment I think not, and, and here is where most people may very well likely disagree with me, I do not think there is a way out of it. What would the successful outcome be here? Could it top the one from FWWM with Laura and her guardian angel? I don't think so. We've never seem the White Lodge really, have we? Can Lynch even visualise it? To me it seems the best we can hope for here is another stalemate with Laura whispering to Cooper in the waiting room.
Thus, my gut feeling at this point is that there is a 15% chance that there will be S4 (probably a four-part series), and 85% that there will not be one. Deadline? Two more years. Hopefully L&F catch a really big fish (for example that S3 was all simply Audrey's comatose dream), and that then gets the ball rolling. Seeing that Matinee Heroes tweet was encouraging, there still is the great cast we have for a new story, and if so, for more than just "Find Laura" from Ray Wise.
Having Desmond in the show could be entirely possible. Any of the Odessa aspects are a stretch for me as they're so specific to that world. Since the characters also are abstractions or alter-egos it all seems even more tenuous. I saw Dougie as Cooper's innocent dream-self. In terms of story and characters, I think any continuing story would have to be as new and fresh as everything in season 3, albeit with more continuity and sense of drama - more akin to the original Twin Peaks in some senses.
I can see that direction being likely after the mostly experimental nature of The Return.
If you only think there is a 15% likelihood of more Twin Peaks, I'm kind of surprised you're even bothering speculating!