OBJECTIVES: I. Determine the safety and toxicity profile, specifically cardiac toxicity, of trastuzumab (Herceptin) following high dose chemotherapy and autologous peripheral blood stem cell transplantation in women with metastatic breast cancer. II. Determine the time to disease progression and disease free survival in these patients when treated with this regimen. III. Determine the impact of trastuzumab (Herceptin) on minimal residual disease after autologous peripheral blood stem cell transplantation as evidenced by serial immunocytochemical analysis of bone marrow. IV. Determine the relationship between posttransplant reconstitution of antibody dependent cellular toxicity and the efficacy of trastuzumab (Herceptin) in these patients.