I think such a story would have to be set waaaaay after the time of Luke Skywalker and Company.
I think a good villain would be a corrupt politician. One that everyone knows is corrupt, but has way too much power to be taken down. When I say power, I don't mean power as in Jedi or Sith power, but influential power. This person would have connections all over the place and control of many corporations whether it is public or not.
To incorporate a Jedi character, you could have the Jedi go through missions and in each mission you discover pieces of some evil plans, but can't really tie it down. Once you have all the pieces you find out that the politician is behind some evil plot (I don't know what, but since it is Star Wars it is probably taking over the galaxy).
I just like the idea of having a "regular" evil dude. Not some insanely powerful Sith Lord.