Combine first 5 ingredients, mixing lightly but thoroughly. Shape into 4 patties. Grill burgers, covered, on an oiled rack over medium direct heat until a thermometer reads 160° and juices run clear, about 6 minutes on each side.
During the last minute of cooking, top each patty with 2 triangles American cheese and 1 triangle Swiss cheese. Serve on buns. As desired, top with lettuce, tomato, onion, bacon, ketchup and mustard.