HEAT oven to 350ºF.
HEAT oil in large skillet on medium-high heat. Add chicken, peppers and mushrooms; cook and stir 5 min. or until chicken is done, adding garlic for the last minute.
ADD pasta, spaghetti sauce, 1 cup shredded cheese and 6 Tbsp. Parmesan; mix lightly.
SPOON into 2-qt. casserole sprayed with cooking spray. Sprinkle with remaining cheeses; cover.
BAKE 30 min. or until heated through, uncovering for the last 10 min.