Give up the squishy white bread. Rye bread is great when grilled. It has an earthy aroma and full flavor. Egg bread tastes even sweeter in a grilled cheese sandwich and a robust sourdough bread is sturdy enough for anything you can pack inside. It's unexpected, but excellent.
Fruit adds moisture to a sandwich.
It complements most cheeses and ham products. Spread with honey mustard. Arrange ham slices over bread. Arrange apple slices over ham, adding just enough to completely cover ham. Sprinkle with cheese.