Yeah, there could be an almost endless variety of grilled cheese sandwiches. In the first season of Throwdown, Bobby Flay went up against a couple who owned a grilled cheese restaurant. I think Bobby made a grilled brie/apple/bacon sandwich.
I make grilled cheese sandwiches all the time. Sometimes basic, sometimes grilled ham and cheese, sometimes I add grilled mushrooms, tomatoes, or onions (or a combo). Sometimes I spread the inside of the bread with marinara sauce, then have cheese and olives.
The menu could be dual. Customers could either compose their own ordering from a selection of breads, a selection of cheeses, a selection of fruits/vegetables, and a selection of meats; or order from a list of specialty sandwiches. Also offer a basic salad or two and a couple of soups of the day.
The one drawback I see to this concept is that it really seems more like a lunch place and less like a dinner place, whereas I can see having soul food for lunch or dinner, or having meatballs for lunch or dinner.