Put the rigatoni in a pot of boiling water. Cook until al dente, about 10 minutes.
Meanwhile, in a medium saute pan set over medium heat, heat 3 tablespoons olive oil. Saute the broccoli rabe stems 1 minute, until softened. Season with salt. Add the broccoli rabe florets and 1/2 teaspoon garlic. Cook until the broccoli rabe is fork-tender, about 5 minutes. Set aside.
In a second saute pan, heat 2 tablespoons olive oil and 1 tablespoon butter over medium heat. Add the spinach, and cook for 5 minutes, covered, until wilted but still green. Set aside.
In a third saute pan, heat 2 tablespoons olive oil over medium heat. Add 1/2 teaspoon garlic, and cook about 30 seconds, until fragrant. Add the Swiss chard, cover, and cook for 5 minutes, until tender. Set aside.
When the pasta is al dente, or firm to the tooth, add 2 teaspoons salt to the water. Drain the pasta into a colander set in the sink. Do not run cold water over the pasta to shock it, as the heat of the pasta is needed to cook the accompanying raw vegetables in the dish.
Place the chopped arugula in a serving bowl. Cover with the hot, drained pasta. Sprinkle the cherry tomatoes, black olives, sun-dried tomatoes, and capers on top. Season with freshly ground black pepper and coarse salt, and drizzle with balsamic vinegar. Toss and serve in individual pasta bowls.
Gently rewarm and taste the broccoli rabe, spinach, and Swiss chard before serving. Place a small mound of each green in a circle on individual plates. Serve either as a first course or alongside the pasta.
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