To a large mixing bowl, add the cooled pasta, tomatoes, peppers, chicken, olives, cheese, and basil. Gently toss the ingredients to evenly combined.
Stir in the dressing mixture, tossing evenly until everything's combined and creamy.
If the mixture's still not creamy enough for you, add a little extra Italian dressing, stirring to evenly combine.
Taste and salt & pepper, to taste. Seal the mixture, either with plastic wrap or in a tupper ware, and refrigerate until chilled, and/or ready to serve.