In a large bowl, combine the cauliflower, broccoli, grapes, onions and mozzarella cheese. Combine the mayonnaise, Parmesan cheese, sugar and vinegar; pour over vegetable mixture and toss to coat.
Cover and refrigerate for at least 2 hours. Just before serving, stir in bacon. Transfer to a lettuce-lined bowl. Garnish with grapes if desired.
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