In a deep bowl, combine the bread crumbs, 1/4 cup of cornstarch, and the coconut, and set aside.
Combine the piña colada mix, the powdered sugar, and the rum in a small mixing bowl and set aside. Place the 1/2 cup of cornstarch in a separate bowl.
Heat the oil for deep frying. It should be at 375° for frying shrimp. Coat the shrimp twice as follows: First Coating: Cornstarch, then in the piña colada mix, then coat in bread crumb/coconut mixture. Second Coating: Piña colada mix, and then the bread crumb/coconut mixture.
Place the prepared shrimp carefully into the hot oil and fry until golden brown. Remove from the fryer and drain. Serve with the piña colada sauce.