Grease a baking dish and lay four pieces of the phyllo pastry, brushing each one with oil and butter. Grate the graviera and crumble the feta and anthotyro with a fork. Mix the three cheeses and add pepper. Divide the mixture into three parts.
Sprinkle one part of the cheeses over the phyllo in the dish, place another phyllo on top, add cheese, cover with phyllo. Add the last portion of cheese and then cover the pie with four pieces of phyllo pastry, brushed with oil and butter.
Score the surface of the pie into diamond shapes, beat the eggs with the milk, a bit of salt and the remaining oil, and pour over the pie. Place in the oven to bake for 50 to 55 minutes at 200° C.