Well my first thought was the multiverse thing that has been suggested by a few of us in the past, but Z beat me to suggesting it here. For the record my roster would've been Karen, Sideways (rookie), Wally West (contemporary), and Lady Quark (veteran, maybe renamed Queen Quark?).
My second thought was "Karen exploring space!" but that's been suggested too. For the record, my roster would've been Karen, Starfire (contemporary), Captain Comet (veteran), and Blue Beetle (rookie, if we can still count Jaime as a rookie?).
So my official suggestion will be......
RAO ("Rectifying Abundant Offenses" or something; I dunno, acronyms are dumb)
Roster: Karen, Nightwing (contemporary), Giganta (veteran), Anarchy (rookie), Major Disaster....probably a few other characters if I sat down and actually thought about this for a few minutes. Kate Spencer, maybe not as a member but as the team's official lawyer......
Base of Operations: Some cool sci-fi Bond-esque mansion-bunker in the Alps.
What's this, you ask? Power Girl and Nightwing leading a team of villains? Well, this here is sorta like the heroic community's version of a "get out" program. Villains who don't really want to be villains anymore but who are in too deep to just walk away work with Karen and Dick and learn how to live clean while getting assistance in escaping from the criminal fraternity with their skin intact (new identities, etc). You ever see those shows or documentaries about the gang member who wants out? This would be the superhero version.
Yeah I know, it's not really a great fit for Karen, but the good ideas were already posted.