Cohorts of 3-6 patients receive escalating doses of flavopiridol until the maximum tolerated dose is determined (MTD). The MTD is defined as the dose preceding that at which 2 of 3 or 2 of 6 patients experience dose-limiting toxicity. Once the MTD is determined, an additional cohort of 10 patients receives flavopiridol at the MTD and trastuzumab on the once weekly schedule to assess the true toxicity rate. A second cohort of 10 patients receives flavopiridol at the MTD and trastuzumab once every 21 days to assess the tolerability of this schedule.