Trim fat from steaks. Marinate steaks in Italian salad dressing overnight in the refrigerator.
Preheat oven to 350 degrees.
Put mozzarella, Swiss and parmesan cheeses in a food processor bowl. Heat oil in nonstick skillet; add bread cubes, toss and saute until brown. Sprinkle cubes with additional parmesan. Put three-fourths of the browned cubes in food processor with the cheeses. Pulse twice only. Remove.
Drain the marinade from the steaks and place them on wax paper. Discard marinade. Press a handful of the cheese mixture carefully on each steak. Place steaks in a baking dish, leaving plenty of room around each steak. Bake 20 minutes for medium, 25 minutes for medium-well.