Heat grill to medium heat.
Mix barbecue sauce and steak sauce. Mix 1/4 cup with meat; shape into 8 (1/2-inch-thick) patties.
Grill patties and vegetables 10 to 12 min. or until burgers are done (160ºF) and vegetables are crisp-tender, turning and brushing with remaining sauce after 6 min.
Top burgers with Singles; grill 1 min. or until melted. Fill buns with vegetables and cheeseburgers.