The problem with the group is that by 1970, they'd grown as individuals immensely. It's not even ego, but just talent and quality. They'd grown so much as individuals that they could only get everything out that they wanted, and pursue what they wanted, as solo. That's the problem with Supergroups, and the Beatles had evolved into a borderline supergroup. The thing that held them together was that they knew each other, liked one another, had worked with one another, and had been together for a decade or more. The Beatles were even on the brink of breaking up in 1966 when they stopped touring. 1966 was a Hellish year for the group (look it all up if you're interested in all the crap that went on), and they'd gotten tired. Lennon was losing faith and reevaluating his priorities, and George Harrison was thinking of leaving after the Candlestick park performance. And they'd gotten tired of a lot of things about being Beatles, which is why they stopped touring. And music was also evolving around them as well. It was getting harder (for the time) and psychedelia was beginning, and critics weren't sure if the group would continue along with the trends and keep up. They did keep up, of course, and continue to set trends, and their solution to their problems was to quit touring. That kept them from splitting in 1966/1967. But what can they do for 1970? Paul's solution, with spearheading the idea for Let it Be, was to get back to an earlier, basic rock and to tour again, and rather than going forward, it was to recapture something previous, and it didn't work. The only place they thought they could go at that point was apart.
I think if you want to keep the Beatles together, you have a few options.
First, let them each release solo albums like the KISS band members did in 1978; technically stated to be Beatles albums, but really solo albums. And then, have everyone return to working with the group once they got that out of their system.
Two, disband the Beatles per OTL, but have them reunite later. They could have very well done this had Lennon not gotten back with Yoko after his lost weekend, or had Lennon not get shot and get back with them in the 80s. I could very well see the latter, since everyone from the 60s had sort of a strong second wind in the 80s.
Three, turn the Beatles into a secondary interest. Have everyone go solo per the OTL, but occasionally gather to release a Beatles album. Or, have both careers go on about equal.
I personally don't want them to stick together in the way most people think of just having them not split at all, because I think they'd be miserable. I think they needed at least a few years on their own and then a reunion.