ARM I: Patients receive docetaxel intravenously (IV) over 60 minutes, carboplatin IV over 30-60 minutes, trastuzumab IV over 30-90 minutes, and pertuzumab IV over 30-60 on day 1. Treatment repeats every 21 days for up to 6 courses in the absence of disease progression or unacceptable toxicity. Patients enrolled after Amendment #4 undergo 2 core biopsies prior to course 3 of treatment.