Left over mashed potatoes can make a mean potato gnocchi, that’s one of my favorite ways to mix it up with extended uses for mashed potatoes. The question you asked has been a part of some of the American Culinary Federation workshops we did last year, which led to reports like "Repurposing Leftover Idaho Potatoes Boosts Creativity and Profitability."

Locally in Idaho, Chef David Knickrehm (previously Executive Chef CEC at Bella Aquila) made several recipes with leftover Idaho mashed potatoes, such as Horseradish Gnocchi. As an added bonus, here is a recipe he has for using left over Baked potatoes:

Idaho® Potato Salad
Yield: 19 5-oz. servings.

• 20 leftover baked Idaho® potatoes
• 5 stalks celery, diced
• 8 eggs, hard-boiled, peeled and chopped
• to taste, salt and pepper
• ⅓ cup minced garlic
• 7 cups tartar sauce
• 1½  cups brown sugar
• 1 cup Dijon mustard
• 1½ cups stone-ground mustard
• ¼ cup liquid smoke
• 1 bunch scallions

Dice potatoes. Combine all ingredients. Allow to sit refrigerated overnight to allow flavors to mingle.