Tuna melts are one of my faves... but not exactly a grilled cheese sammy.
When I want to jazz up a grilled cheese sandwich, I spread some pesto on the bread, add muenster, swiss, mozzarella (whatever cheese you like), top the cheese with sun-dried tomatoes. In place of the pesto, top the cheese with fresh basil leaves. If you want to get fancy, press some toasted pine nuts into slices of mozzarella, rub the mozzarella or bread with a garlic clove, and saute in evoo/butter.
Mozzarella in Carozza (Mozzarella in a carriage)
Place a slice of mozzarella on white bread, top with another slice of bread (trim the crusts), dip in an egg/milk mixture (add some flat leaf Italian parsley to the egg mix, if you like), and dip again in Italian bread crumbs, and fry it up.
Instead of a plain ole ham and grilled cheese, try mozzarella, proscuitto, sun-dried tomatoes, and basil leaves -- or Monte Cristos.
I posted a recipe a while back for Mozzarella S'mores. Use slices of garlic bread in place of sandwich bread. Foccacia is another way to go.