Whisk together the olive oil, vinegar, shallot, 1/2 teaspoon salt and a few grinds of pepper in a large bowl.
Cook the lima beans in the boiling water until tender, about 15 minutes. Add the corn and continue to cook until the corn is tender, about 2 minutes more. Transfer the beans and corn to a colander with a slotted spoon and run under cold water to stop the cooking process. Drain well and add to the bowl with the dressing.
Add the pasta to the boiling water and cook according to the package directions. Drain and rinse under cold water to cool; add to the bowl.
Add the crabmeat, celery, chives and parsley to the bowl and toss to combine. Season with salt and pepper. The pasta salad is best if served right away.
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