Mario 100% should not be a stance character because he needs to be beginner friendly and the mechanic is pretty antithetical to that. The idea of power ups changing neutral special might work since it does for Kirby (but Kirby uses game design techniques that teach you how abilities work that wouldn't apply here), but even then it's hard to come up with a way to change his neutral special that wouldn't be kinda awkward to use.
If we were to implement power up mechanics, I'd give him a standard meter that gives him the Fire Flower when you fill it. You could make the meter function similarly to how the mechanic works in its home series as well by having it reward combos with more meter, and taking damage would remove it, or something along those lines.
Beyond that, perhaps his smash attacks could use certain power ups? It'd really depend on which ones used in what way since I don't think it would work at all if it required a costume change, but you'd have a bit more leeway there.
What I'd really like to see is Toad and/or Captain Toad added as the stance character that explores the design of Super Mario Bros.'s power up mechanics. Since this time of move set wouldn't work for Mario, or by extension, Luigi, Toad seems to be the next best thing since he's about the only other character that's tied to the main series and doesn't have a whole lot else going on. I mean, Captain Toad has the no jump thing, but that's not a great mechanic for a platform fighter anyway, and they could easily reference it with a higher weight value for his size, and a low jump height, which playable Toads consistently have anyway. Toad also isn't beholden to representing the series in its entirety, so they're free to pick what works rather than what's currently relevant (especially since it's not a whole lot, and what's relevant now won't be in a year or two).