Prepare the salad up to 1 day ahead, and store in the refrigerator. If you can't find fresh cranberry beans, substitute rinsed and drained canned cannellini beans, and add them to the snap beans for the last 2 minutes of cooking.
Combine cherry tomatoes and next 8 ingredients in a large bowl.
Combine 8 cups water and cranberry beans in a large saucepan; bring to a boil. Reduce heat, and simmer 15 minutes or until tender. Add green and yellow beans; cook 5 minutes or until crisp-tender. Drain and rinse with cold water; drain well.
Add bean mixture to tomato mixture, and toss gently to coat. Sprinkle with shaved cheese.