The only possible story they can tell is a "backsliding" story: either the Grinch or Whoville somehow goes back to the way they were at the start of the first movie.
The sequel becomes just another re-telling of the same story, with either the Grinch or the Who's (or both) having to be re-enlightened with the knowledge they temporarily received at the end of the first movie.
The ending will of course be a "happily-ever-after-now-we-really-get-it" conclusion...until they want to make another sequel.
I'm serious. There is no more story to tell about him. In fact, the only other time I saw him in Dr. Seuss lore was on a cartoon about a nerdy who teen that ran away from home (or rather, was blown away from home by the wind), and the story wasn't even taking place during Christmas time! And for some strange reason, everyone kept telling the kid to put his glasses back on, including the Grinch!
The only thing I can think of is a brief scene of his and Martha May's kids, hehe. They could do cartoon genetics, where all the girls are pretty blond Who's like Martha, and all the boys are green and hairy like dad xD