Since this is going to be the last of a trilogy, where it goes next is wide open. Totally new actors, completely different focus. Anybody's guess.
Yeah, there are a number of things Fox could do. If I had to guess, I think they'd use the whole "new timeline" thing happening between DoFP and Apocalypse and do a Star Trek-esque reboot. It's technically within the same universe as the previous films, but an alternate reality/dimension/whatever. This leaves them free to recast the main bunch, but (if they have to) occasionally bring in one of the old dogs for a quick cameo or whatever.
Hopefully they're watching how Sony utterly botched their Spider-Man franchise with a sloppy reboot and are looking for ways to actively avoid that. Fox have had to dig this franchise out of the gutter once already, and the X-Men are flying high once again. They probably don't want to squander the good will the X-films have regained thanks to DoFP (and to a lesser extent, The Wolverine).