In a medium bowl, combine the shrimp with 3 tablespoons of the dressing and toss to coat. Thread shrimp onto skewers.
Place skewers on grill rack directly. Cover and grill for 3 to 4 minutes or until shrimp are opaque, turning once halfway through cooking. Remove from grill; set aside on a large baking sheet.
Place corn on the grill, and cook, turning frequently, until corn is lightly charred and heated through, 8 to 10 minutes. Remove from grill; when cool enough to handle, cut kernels from cobs and transfer to a large bowl.
Remove the shrimp from the skewers and add to the bowl with corn, drained tomatoes, green onions, mozzarella and basil and remaining dressing. Season to taste with salt, pepper, and more balsamic vinegar, if desired.
Nutrition information per each of 6 servings: