***I kind of like the idea of a team of X-Men that do not have an X-Mansion. A team that lives in the Bronx to help the every day mutant. I like the idea of a more humble headquarters that could just be an apartment building(Sure a bit more advanced but something not far from the people.) Funded by...Warren Worthington
I think a "Street Team would consist of:
Bishop - The guy used to be a cop...maybe being a bridge between local law enforcement and neighborhood mutants would not be the worst thing ever.
Catiana - NYX girl. She knows the neighborhood, she wants to help people and she like the idea of living in the headquarters rent free.
Ricochet - Wants to help people but isn't trying to go to space or on massive huge adventures like the other X-Teams...he wants to keep things local.
Doctor Celia Reyes - Every team needs a medic.
Gargil - Every team needs muscle.
Prodigy - The Man in the van, tech guy.
Cloak and Dagger -
It all comes down to how common you want to make mutants because generally, I don't really think there should be that many mutants in the Bronx. The X-Men's mission isn't a local one. It's global and spread far and wide. Even something like the Morlocks is very problematic.
But if we were using Morrison's model, a place like the Bronx would have about 6700 mutants in it (mutant population was approximately 1:250). I might enjoy that as a satellite team... preferably, them not being called X-Men.