Star Trek made a lot of fans happy not too long ago when Strange New Worlds and Lower Decks crossed over for some shenanigans. The crossover took place in Strange New Worlds' second season and saw two of Lower Decks' best; Brad Boilmer (Jack Quaid) and Beckett Mariner (Tawny Newsome) go from animation to live-action.
It was an episode fans loved, and many had hoped for more in the coming years but recently, Trek higher-up and legendary actor and director Jonathan Frakes has seemingly put the kibosh on any future crossovers. At least for now.
Speaking to TrekMovie.com's podcast, Frakes revealed that Alex Kurtzman doesn't seem too keen on doing any more crossovers, saying;
"“I think the (crossover) show did so well. You know, [co-showrunner] Akiva [Goldsman] would would certainly take the swing like that. I think [co-showrunner] Henry Alonso Myers would too. I’m not sure how Paramount Plus or Alex [Kurtzman] would feel about it, but it worked.”"
The fact that Kurtzman's views on a further crossover seem unknown suggests that Kurtzman may not be as on board as Frakes and others. Considering the financial situation at Paramount+ and Paramount Global as a whole, this isn't surprising.
The only Star Trek show that Paramount+ has any say over at the moment is Strange New Worlds, and if Netflix greenlights a third season of Prodigy, they would likely have the final say if those characters could be used on a Strange New Worlds or vice versa.
With the franchise seemingly toning down television shows on the service to the point that only Strange New Worlds exists and instead focusing on cheaper Star Trek films to make, the likelihood that another Trek series crossovers over with Strange New Worlds, or even beyond isn't very likely to happen.
Now, things can always change but right now it doesn't seem likely that a genuine, character-focused crossover, will end up happening again in the immediate future.