This may be a hot take, but I think an Adventure mode closer to Melee's might be ideal for Smash. Keep it short, and that way the variety stands out more. Each section can have Smash lean into that specific property's hook. You know, platforming (both horizontal and vertical), a Metroidvania, a 1v1 stamina fight, a race, using items, something arcade-y, collectathon, king of the hill/hold the line, survival mode, run n gun, stealth. You could even do something turn-based, if its slower pace didn't prove too disruptive. In one playthrough you could run not just through different IPs, but in a sense, different genres.
And it'd be a great place to fit in the boss fights. Melee didn't really have any, besides the hands and Giga Bowser.
Each section could have two phases, one that reflects the series, the other the traditional Smash battle against that IPs' character(s). Then each character could have a different selection and order of the sections to keep Adventure mode unique based on character, and to reduce repetitiveness. Maybe difficulty scales with their placement, like a Mario level having more/tougher enemies if towards the end. Plus if a certain character would somehow break a certain level, they just wouldn't get that one. Which would in turn help the level design, not having to balance it for the entire cast.
If you really wanted to embrace the crossover aspect of Smash, you could merge multiple IPs into a single section, if they overlapped gameplay-wise. Like, if there was a Metroidvania level, part of the maze could be a sci-fi alien planet, and part could be a gothic castle, with enemies from both. One level could be a fighter arcade mode, and pit you against Ryu then Terry then Kazuya (even Min Min and Little Mac), and have arcade-like intertitles between fights. One level, you collect all the dots and avoid the ghosts, like Pac-Man. Except it's not Pac-Maze, it's a level from arcade Donkey Kong, and he's at the top, chucking barrels at you. The power pellets make him vulnerable as well, and if you attack him, he'll quit chucking barrels for a while. If you do enough total damage, he'll **** off entirely. Then maybe you don't have to fight DK in the next round. The bonus fruit heals you, maybe pong/sheriff/galaga also show up to cause trouble. Or there's a level where it starts on Mute City and you have to dodge the racers like Melee, then the course transitions to a Sonic stage, you get one of those speed boost item boxes
and you have to
outrun the racers. Then you get to a launch star or a big spring, and it shoots you upward. Now you're on Rainbow Road, and you have to outrun the racers while
also dodging Shy Guy drivers.
You could write a whole list of possible ideas for levels, whether individual or mixed.
If each path per character is completely predetermined, you could then fit short interactions between certain characters in there. Even if there was a degree of randomness in which sections are selected and/or their order (within a pool for each character), you could still have interactions between some matchups, they'd likely just be shorter given there'd be more. And then you'd have replay incentive to find them all.
Such a thing would compliment a possible recruitment mechanic, where you could recruit one or more defeated character(s), either just as a CPU ally for fights, or as a one-off 'extra' life you can switch to. Depending how they want it to work. Since each path is predetermined, you wouldn't have to create interactions for every possible combination of characters.
You also don't have to worry about juggling a story featuring dozens of characters, so you could just pick interactions that would make sense instead of whatever the plot dictates. Like two characters that actually speak, so there could be dialogue instead of reducing one to grunts and miming because the other idiot can only go 'wahoo!'.
And you could also gradually reveal levels during pre-release like with the other content.
It's more realistic than dedicating the budget to another SSE again, complete with a movie's worth of cutscenes. The engagement versus cost isn't there.