Combine first 11 ingredients in a stock pot. Bring to a boil, lower heat and simmer for 1 hour covered. Combine ground beef, chicken, sausage in a saucepan. Cook until done and add to tomato mixture. Simmer for another 20 minutes.
Layer bottom of a 13 by 9 by 2-inch pan with sauce. Add a layer of angel hair, pinch cream cheese over pasta, place a single layer of Swiss cheese, then 1/2 of Cheddar and Jack cheese, repeat layers ending with sauce. Bake in a 350 degree oven for 30 minutes. Top with remaining cheese. Return to oven and continue to cook until cheese is melted. Cut into squares before serving.
Recipe courtesy of Paula Deen