Mix lime and orange juices.
In each of 4 tall glasses (12- to 14- oz. size), make a layer of 1/4 cup pineapple. Add 1/4 cup jicama and top with 1/4 cup mango.
In a bowl, combine the remaining pineapple, jicama, and mango, and spoon the mixture equally into each glass. Pour the lime-orange mixture equally into each glass.
Top each serving with hot sauce and chili powder to taste, and sprinkle with 1 tablespoon cheese.