Cook bow tie pasta, medium pasta shells, and wagon wheel pasta according to package directions until al dente.

Drain the pasta and rinse with cold water to stop the cooking process.

Drain the pasta well to remove excess water.

Transfer the cooked pasta to a large bowl.

Add Greek vinaigrette to the pasta and toss to coat evenly.

Add halved cherry tomatoes, finely chopped red onion, drained and coarsely chopped marinated artichoke hearts, and drained and chopped roasted sweet red peppers to the bowl.

Add chopped fresh basil, grated Parmesan cheese, sliced pepperoni, and drained sliced ripe olives to the pasta mixture.

Toss all ingredients together until well combined.

If desired, transfer the pasta salad to covered jars.

Refrigerate the pasta salad until serving to allow flavors to meld.