I would rework the entirety of the X-Men mythos if I could. I'll also post about one character in particular next (pic related), so that I stay on-topic with the thread.
I love the idea of "species" of mutants, it makes them make more sense to me. We have so many examples of Mutant lineage actually mattering in what powers are passed on, so it already fits. Give them some consistent traits, and establish HARD limits on what they can do, and make them consistently weaker than their other super-being counterparts (the way they used to, like when Spider-Man could take out the entire team alone). Of course, there would be sub-groupings within the "species" as well.
The different types of mutants could be:
>"Logans" - Feral instincts, animal-esque traits, healing factor that extends lifespan (Wolverine and Co., Beast, Wolfsbane, Angel, etc.)
>"Apocalyptians" - Powers that involve their own individual genetic timelines, including a sort of time travel that involves assumption of previous and future selves, ancestors, and/or descendants (Apocalypse, Gideon, Mister Sinister, Madrox, etc.)
>"Summerses" - Energy blasters and/or manipulators, often unable to harm other mutants or those related (or something similar) (Cyclops, Havoc, Gambit, etc.)
>"Manipulators" - (also called JEANNNNS) Those with telepathy and/or telekinesis, and includes all shapeshifters and elementalists, both literal and psychically-projected (Emma, Professor Xavier, Magneto, Mystique, Pyro, etc.)
>"Hunters" - Those with the ability to influence other Mutant's powers, whether stealing them, copying them, or shutting them down and/or powering them up (M, Rogue, Leech, Caliban, Callisto, etc.)