Add liver; simmeruntil broth measures 4 cups,about 30 minutes longer.Strain; reserve broth. Pickmeat from neck and chopgiblets; set aside.
Preheat oven to 350°F.Butter a 2-quart baking dish.Cook sausage in a large skilletover medium heat untilbrowned and cooked through,about 10 minutes. Chopparsley leaves and remainingcelery in a processor.
Add neckmeat, giblets, and sausage;pulse just to combine.
Transferto a large bowl; add stuffingmix.
Add turkey broth by1/2 cupfuls, mixing until moistbut not wet. Season withsalt and pepper; transfer toprepared dish.
Cover dish with foil.
Bakeuntil heated through, about 40minutes. Uncover; dot withbutter and bake until browned,about 20 minutes longer.