Mix relish and 2 Tbsp. steak sauce. Shape meat into 4 (1/2-inch-thick) patties.
Grill patties and onions 4 to 5 min. on each side or until burgers are done (160F) and onions are crisp-tender, brushing occasionally with remaining steak sauce. Top burgers with Singles; grill 1 min. or until Singles begin to melt.
Fill rolls with lettuce, cheeseburgers, onions, tomatoes and relish mixture.