If they followed a GTAV or RDR2 model (robust, fully realized SP with optional online which is its own thing) I'd be fine with that. Otherwise, no thanks.
The issue here is that Bioshock's general gameplay design doesn't really mesh well with that specific kind of support. GTA and RDR are open worlds with a lot of ways to have all kinds of ways to play. Bioshock 1 and 2 borderline on Metroidvania with intricately designed locations that you explore as you get more abilities, and Infinite is linear Daughter Simulator that mechanically is a big step down from 1 and 2, aside from Elizabeth herself being a (at the time) fairly well designed companion.
I think the only stuff that you could realistically do with Bioshock and keep what people like about the old games is a Horde mode, or maybe a more traditional versus mode, that that didn't really set the world on fire back in Bioshock 2.
If you expand it to something more akin to Destiny or Warframe, I think mechanically it can be done because of the way Plasmids and Vigors work, as well as the lore of having tons of Splicers down in Rapture. The issue is you simply can't make the rest of the game feel right with that set up. It would fundamentally be different from what people liked about the series in the past, and you end up with a game like Dead Space 3 or a (hypothetically bug-free) Fallout 76.
That just made me incredibly sad. The only progression system I want out of a Bioshock game is a great story. Keep the Destiny bull crap out.
To be fair here, Bioshock does have progression in all three games. You decided how to upgrade both your weapons and Plasmids/Vigors to some degree, though it was less well thought out in Infinite than the first two.