I don't think they will, but it's entirely possible that Doom Patrol and Titans could crossover without the multiverse. Either particular universe, Earth-9 or Earth-21, could simply have the same doubleganger, and either one could be the true universe, while the other might just be similar.
Personally, I believe that, pre-crisis, Titans and Doom Patrol were in the same universe, but post-crisis, the universes split into two, with one history going with what we see post 10 December 2019 in Titans, which hasn't happened yet, while the other is post December 10 in Doom Patrol, everything after Doom Patrol 1x15. This way they can play it off as separate realities while also making sense of the references between them. I wouldn't treat it that way officially, but it makes sense to me.
I feel it's more likely that Stargirl would crossover with the Arrowverse, although I don't think it should become apart of that "franchise" so to speak, seeing as it's a different universe and the whole point of Earth-Prime was to stop that sort of thing