Hm. Both cities (Steelport, Stilwater, maybe connected with a reconstructed Hughes Memorial Bridge) and a lot of area.. then throw in some sort of hood control thing, allowing people in part to make their own gangs. You'd have to figure a way to cleanly random gen stuff to do, without going to the madlibs Skyrim style, or the reused triggered GW2 style.. hm. Like they keep promising with 'dynamic changing events'. Maybe more akin to say EVE Online's dynamic unscripted thing.
Then figure a way to let people get across the areas. I'm not so sure about how you'd handle any sort of 'mmo' bit, you'd need an upgrade path but what, akin to the unlocks from SR3/4? Modified maybe.
Biggest problem is adding the content etc to make it feel more than just "third person online group shooter/thing in Saints Row areas". Missions, etc. That'd be a fun challenge.
It's doable, I guess. Would it be impressive? Yes. Would it sell? Hell no! Even forgetting that MMOs probably have a success rate comparable to kickstarters, there's not enough die-hard fans and general fans and even general likers who'd buy into the game. You either subscription model it (good luck, there's a reason almost no one does that nowadays) or monetize the SHIT out of it and hope you can break even for dev costs. Plus, no publisher wants to go for an MMO, they always can them before release because it's apparent it's not gonna work. As much as it would be fun, I can't imagine this happening.
But I would LOVE something akin to multitheft auto for Saints Row 3/4, particularly something with the more in-depth lua scripting. Heck, the game runs on lua to begin with, so expanding the call set is always worthwhile.