Butter one side of 4 pieces of bread. Place on grill, butter-side-down. Cover with Thousand Island dressing. Lay 2 slices of cheese on each piece of bread in such a way as to cover the dressing. After bread is grilled, place in oven to finish melting the cheese.
Meanwhile, butter remaining 4 pieces of bread. Place on grill. Cover each with Thousand Island dressing. Cover each piece with 2 turkey slices, or more if desired. Lightly coat turkey with Thousand Island dressing. Grill until heated through. Remove from grill. Place the pieces with the melted cheese on top of the turkey, cheese-side-up.