Cook spaghetti according to the package directions. Meanwhile in a large bowl combine the chicken,cream of chicken soup,onion,milk,1/2 cup cheddar,1/2 cup swiss,mushrooms,peppers,mayo,steak seasoning and basil.
Drain the spagetti; add to chicken mixture and toss to coat.
Transfer to a greased baking dish. Cover and bake at 350 for 20 minutes. Uncover and sprinkle with remaining cheeses.Bake 5 to 10 minutes more to melt cheese.