Using an electric mixer, beat the cream cheese at high speed until light and fluffy. Lower the speed and add the ricotta, cottage cheese, 1 1/2 tablespoons sugar, and the nutmeg. Beat for 1 minute at high speed, then set aside while you prepare the filo. Lay the filo flat on a table and keep covered with a damp towel over waxed paper or plastic wrap.
By stacking 4 sheets, form a base of 15 x 18 inches, brushing the top of each sheet with melted butter as you stack them. Then lay 2 sheets at right angles over the center, using the "base" as a diamond, not a square, brushing the center of each with butter. Divide the filling into 3 parts and spread one part over the filo to form a 7-inch square. Set the rest of the filling aside.
Fold the top filo sheet over the cheese and brush with butter, and continue folding the filo over the cheese to make a square, brushing each time with butter. With a wide spatula, lift the bougatsa and invert onto a cookie sheet. Brush the top with butter and set aside.
Repeat with the remaining filo, filling until all 3 square pies are folded. Bake in a 350 degree oven for 15 to 20 minutes or until the filo puffs up and turns a golden chestnut color. Cut into small squares and sprinkle with additional sugar. Serve piping hot.
