Place the phyllo sheets on a work surface and cover them with a dampened towel. Melt butter and olive oil together in a small pot. Combine all the cheeses in a medium-size mixing bowl. Brush half the oil and butter mixture evenly onto the bottom of a cookie sheet or half-size sheet pan. Begin to layer the phyllo sheets one at a time, brushing each layer with the butter mixture. Sprinkle 3 tablespoons of cheese between every second sheet (5 times). Repeat until all 10 sheets have been used. Brush the top layer with the butter mixture. Use half of remaining cheese to sprinkle over top, leaving ½ inch of edges of phyllo sheets exposed. Add scallions and basil and lay the thinly sliced tomatoes side by side. Sprinkle salt and pepper (to taste) and remaining cheese over all. Bake for 20-25 minutes, or until phyllo is golden and cheeses are melted. Let rest 5 minutes before slicing.