The BTTF movies always hinge themselves on the fourth-dimensional idea that time is linear, and that any changes we make can result in universe-destroying paradoxes. But I found if you approach the BTTF trilogy from a fifth-dimensional perspective (fifth-dimension, in this case, being infinite probabilities, where paradoxes are corrected by the means of multiple time-lines, so no one can ever be erased from history) the trilogy actually ends halfway through the second movie.
The first movie is fine. By accidentally traveling back in time from 1985-A, and accidentally changing the past, Marty ends up in an alternate 1985-B where his 1985-B counterpart has also accidentally gone back in time, stranding the 1985-A Marty with the 1985-B family. Marty's original time-line (1985-A) is still intact, but Marty can never return to it.
In the second movie, Doc arrives from 2015-B where Marty Jr. is arrested, but then by bringing Marty along to stop it, he changes lanes into an alternate 2015-C where Griff gets arrested instead. So far, so good, because they can still return to the 1985-B they left from, and 1985-C would pick up from there.
But then Biff steals the Delorean and goes back in time to 1955-A with the Almanac. By changing the past, he would create a completely separate 2015-D to return to where Marty and Doc don't exist. They'd still be trapped in 2015-C after rescuing Jennifer and wondering where their car disappeared to.
So even if Doc built another time machine in 2015-C, he, Marty and Jennifer wouldn't travel back to Biff's 1985-D because that time-line is only accessible from 1955-D. They'd just wind up back in 1985-B and their adventures would end. No cowboys, no Clara - just Marty and Jennifer going to the lake. Meanwhile Biff would grow fat off his money in 1985-D, and Old Biff would spend the rest of his days joy-riding around in Doc's Delorean, creating tons of new time-lines and probably having lots of adventures.