PHASE I: Patients receive oral vorinostat twice daily on days 1-14 and trastuzumab (Herceptin®) IV over 90 minutes on day 1. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. Cohorts of 3-6 patients receive escalating doses of vorinostat until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 3 or 2 of 6 patients experience dose limiting toxicity. At least 6 patients are treated at the MTD.