I'm no expert on the band, but I do think the Beatles offer a unique oppurtunity from an Alt History perspective. They were already more or less three solo artists doing their own thing by 1968, so any hypothetical 70s Beatles albums wouldn't likely sound too different from a playlist of songs from their various solo albums. A full on breakup doesn't seem inevitable either. Getting all four Beatles to stick around would be a major challenge yes, but continuing on as a trio, most likely with John leaving, seems very plausible. I believe this was actually discussed as a possibility OTL. Paul desperately wanted to keep the group together, George would get more songs without John taking up a good chunk of album space, and Ringo might even be able to get a song in now and then. John could be all artsy fartsy with Yoko and not piss off the rest of the band, and the fans still get a band recognizable as the Beatles for a longer period of time. It's a good situation for everyone.
How plausible do you think each of these scenarios are?
The band continues on as a four piece. (Doable I suppose, but very difficult. John would still likely leave in the mid 70s anyhow.)
John leaves, the other three carry on. (Seems the most likely alternative to me, for the reasons above.)
Paul leaves, the other three carry on. (Hard mode.)
George leaves, the other three carry on. (SUPER DE DUPER HARD MODE!)
Ringo leaves, the other three carry on. (Ringo was the one that broke up the band all along!)