The All-New Mutants
Original New Mutant Karma would lead the Jean Grey School for Higher Learning's school team, with Jubilee acting as the field leader/combat instructor. The team's primary tasks are to rescue, protect, teach, and train new mutants, in that order. The team is rounded out by graduate X-men Armor, Cipher, and Rockslide, as well as Hijack, who stays on as the team's tech-savant/babysitter. This team would share the school with the X-men, but mainly only for context.
Prof.Xi'an- One of the ideas I had for why Karma would decide to take on Xavier's former role would be because of the death of one of her students that she feels she should have been able to prevent. This would be the real impetus for her reaching out to Jubilee to form the New Mutants action squad that makes the school it's priority.
As the name implies, this series would also primarily be about newer/younger characters at the school, most of whom are not specifically training to be X-men. The initial class would be comprised of Goldballs, Oya, Eye-boy, Nature-girl, and Morph, with No-girl and Ernst as supporting characters. As the series progressed, some new characters would join while others leave. One of the first new recruits I'd like to see is Kid Colossus from the Savage Land, but for the most part I think more grounded characters with weirder powers would be more interesting.
Major Threats: Besides whatever threat is behind Kid Colossus coming to the school, I'd like to see this group come in contact with Shogo's biological father, the Future, as well as Emplate, the U-Men, Super-Human Registration Act advocates, and at least one or two new threats before coming to a story involving the Shadow King's new Hellfire Club sometime in the middle of the second year.