Melt the butter in a large saucepan over medium heat. Stir in the onions, mushrooms, and garlic; cook until tender, but not browned, about 5 minutes. Stir in the flour, sage, and thyme until blended. Pour in the gravy, water, and milk, stirring to blend. Bring to a boil over medium-high heat; cook 1 to 2 minutes. Stir in the turkey and vegetables, and cook until vegetables are tender, about 5 minutes.
