Chemotherapy and Peripheral Stem Cell Transplantation Followed by Trastuzumab in Treating Women With Metastatic Breast Cancer

RATIONALE: Chemotherapy uses different ways to stop tumor cells from dividing so they stop growing or die. Combining chemotherapy with peripheral stem cell transplantation may allow the doctor to give higher doses of chemotherapy drugs and kill more tumor cells. Monoclonal antibodies such as trastuzumab can locate tumor cells and either kill them or deliver tumor-killing substances to them without harming normal cells. PURPOSE: Phase I/II trial to study the effectiveness of chemotherapy and peripheral stem cell transplantation followed by trastuzumab in treating women who have metastatic breast cancer.