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Team Alliance
(Or something similar to that)
They're led by a native to whatever region this takes place in. The entire team is made up of wayward members of the other teams that were beaten, Rocket, Magma/Aqua, Galactic, Plasman, Flare, etc. etc. Basically, any grunt who didn't know what to do with themself after their team fell apart, or any grunt who managed to break out of (pokemon jail?) joined up with this new team.
Their leader offered them a new sense of purpose as Alliance members. The grunts all wear new outfits, but are allowed to have a stripe or something on their uniforms that identifies them as a previous Rocket/Magma/whatever member so they can have a bit of pride in whatever they did last.
The team's four lieutenants are made up of previous members too. Two were grunts from Aqua and Galactic that got named and promoted in the new team. The other two could be returning lieutenants from the previous games, now a bit older and part of Alliance.
I guess their goal is to take over the world or some shit, or maybe it's just to get even with everybody else in general.
I just like the idea of the """""last""""" game in the series having a team comprised of all the other teams, led by a new villain.
Plus, I love talking to grunts after beating them. It would be fun for some to mention their times back in Hoenn or Sinnoh, or making a remark of what life under their previous boss used to be like.
Plus, it would allow for some really diversified teams used by the bad guys. Previous Aqua members have water pokemon, whereas previous Rocket members use dark in conjunction with their new mons. Stuff like that.