Bring a large pot of water to a boil and salt it. Put the oil in a large skillet over medium-high heat. When its hot, add the zucchini and cook, stirring occasionally, until it begins to soften, about 5 minutes. Sprinkle with salt and pepper. Add the tomatoes; cook until starting to soften, about 5 minutes. Add the corn and green beans to the pan and cook, stirring occasionally, until the corn and beans are just tender, about 5 minutes more.
Add pasta to boiling water and prepare as directed. When the pasta is done, drain it and toss with the zucchini mixture and the Parmesan. Taste and adjust the seasoning, garnish with basil if you like, and serve.