I think it's much more common for SMs (and actors) to be doing this when freelancing at different theatres than when working for the same theatre (except actors repping of course).
As an SM, I quite often have overlapping closing week/prep weeks, and have mastered the art of prepping while away from the theatre. It makes for a crazy 2 days before prep, and I usually work on the Monday before rehearsals begin to get the room set up, floor taped, purchase any necessary supplies, etc.
As a non-union SM, I did this quite often, and though it's a different situation, yes, there were many concessions made. Of course, the show I was in performance for had to take priority, so I would have to miss some rehearsals and have the ASM take over.
It's also feasible in a company where there is a staff of SMs that an ASM can cover for other ASMs if one ends up having a rehearsal for another show with the company. The sub could sit in on rehearsal, or if the show was light, be backstage for the show while the other ASM was in rehearsal. I've heard of this being done at one major regional theatre that I've been with. I think it's rare, but does happen.
I don't think, personally, that it would make sense to REHEARSE two differnet shows at once, since there will inevitably be big problems once the shows open.