Preheat oven to 350 degrees F (175 degrees C). Lightly spray a 9x13-inch baking dish with cooking spray.
Spread crushed chips out into the bottom of the prepared baking dish.
Stir chicken, 1 cup Mexican cheese blend, salsa, cream of mushroom soup, cream of chicken soup, and sour cream together in a bowl. Pour chicken mixture over crushed chips into the baking dish.
Bake in the preheated oven for 20 minutes. Spread remaining 1 cup cheese over the casserole and bake until cheese is melted and bubbling, about 5 minutes more.