I could see an argument for another "crossover-themed" series of some kind working well alongside that, with something like Project X Zone probably being the first thing to come to mind (even though, by technicality, it does retroactively have some Smash characters in it already.) That said, I don't think it'd be treated as a dedicated crossover between PXZ and SSB, more likely just that SSB would be represented in the game either more loosely or with a chapter or two with a story inspired by something from the Smash series - for instance, gathering up characters who've also featured in the Smash series to fight Master Hand on a Final Destination location, but in a turn-based format instead.
...I suppose you could also make an argument for something like Mario Kart Tour? Not necessarily leaning into the "Smash Kart" angle, but moreso by including Smash-themed stuff like costumes or whatnot for the Mario cast (Luigi in a Marth costume or Peach in a Samus costume, for instance). But then that's kind of just leaning into a more general "Nintendo crossover".
The difficulty is obviously that Smash itself - that is, Smash-original elements - probably aren't interesting enough on their own to warrant a crossover with it specifically, especially when Smash's biggest-known idea is that it, itself, is a crossover. You could totally represent Smash-original elements, but I think it'd inevitably feel more like a "Nintendo crossover with Smash elements" than anything.
That said, it would be very funny for some kind of gacha game to exclusively crossover with Smash-original elements, resulting in things like a Master Hand boss fight or characters like the Fighting Polygons, the Fighting Wireframes, or the Alloys. That'd probably have worked better back when Brawl was around, though; because of the Subspace Emissary.
(No clue how this would work but it would be cool)