Sauté garlic in hot oil in a large skillet over medium heat 1 minute or until lightly browned. Carefully stir in wine and next 5 ingredients; bring to a boil. Reduce heat to medium low, and simmer, stirring occasionally, 20 minutes or until thickened.
Cook pasta according to package directions; drain. Stir together hot pasta, mozzarella cheese, and 1/3 cup Parmesan cheese in a large serving bowl, tossing to coat until cheeses start to melt. Stir clams into tomato sauce; pour tomato sauce over pasta mixture, and toss to combine. Serve immediately with desired toppings.