Lay pizza crust on a foil-covered pizza pan or cookie sheet. Spread sauce evenly over pizza crust. Sprinkle mozzarella cheese over crust, leaving a 1-inch border around the edge. Arrange prosciutto on top of cheese. Sprinkle goat cheese over prosciutto. Bake until prosciutto is crisp and cheese is melted, about 12 minutes. Sprinkle basil over pizza. Cut pizza into 6 slices and serve.