Add butter to a hot stainless or cast iron skillet and sauté onions and celery until soft then remove from pan and place into a large mixing bowl.
Brown sausage meat in the same pan. Remove and add to the mixing bowl once cooked. Deglaze pan with some chicken broth and add scrapings and broth to mixing bowl.
Brown ground beef in the same pan with some olive oil if necessary. Remove and add to the mixing bowl once cooked. Deglaze pan with some chicken broth and add scrapings and broth to mixing bowl.
Add the bag of stuffing cubes to the mixing bowl.
Distribute the sage and thyme around the mixing bowl and stir.
Add 1¾-2 cups of chicken stock distributed around the bowl and stir gently.
Taste and add salt and pepper and any additional seasoning you want.
Place into a 9x13 or larger pan and bake at 350°F for 30 minutes or until the top has browned. To keep the stuffing moist you can drizzle an additional half a cup of chicken broth over the stuffing while it cooks using a squirt bottle or turkey baster.