Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, 15 to 20 minutes.
While the potatoes are cooking, preheat the oven to 350 degrees F (175 degrees C).
Drain potatoes and return to the pot. Mash while hot. Add sour cream, butter, Parmesan cheese, cream cheese, Cheddar cheese, green onions, salt, and pepper; beat until well blended. Transfer to a 3-quart casserole.
Bake in the preheated oven for 45 minutes. Serve piping hot.