Cook the rice in boiling salted water according to the instructions on the package, stirring often. In a colander, rinse the rice thoroughly under cold water to stop the cooking process. Drain.
In a large bowl, mix together the rice, fontina cheese, mozzarella, scamorza cheese, cherry tomatoes, olives, capers, and anchovies. Toss well.
Add the olive oil and salt, to taste. Let rest for an hour in the refrigerator before serving.