OUTLINE: Patients begin study treatment within 50-150 days after autologous or syngeneic peripheral blood stem cell transplantation. Patients are stratified according to overexpression of HER2-Neu (yes vs no), which determines the type of therapy. Arm I (overexpression of HER2-Neu): Patients receive paclitaxel IV over 60 minutes followed by the initial loading dose of trastuzumab IV over 90 minutes. If the loading dose is tolerated well, then patients receive maintenance trastuzumab IV over 30 minutes. Treatment with paclitaxel followed by maintenance trastuzumab repeats once every week for 12 weeks in the absence of disease progression or unacceptable toxicity. Arm II (no overexpression of Her2-Neu): Patients receive paclitaxel IV over 60 minutes once every week for 12 weeks. Patients with hormone receptor positive disease also receive antihormonal therapy (tamoxifen or anastrozole) as clinically indicated. Patients with isolated metastasis such as a single bone lesion may receive radiotherapy to that site after completion of study treatment. Patients are followed every 3 months for 1 year, every 6 months for 2 years, and then annually thereafter.