OUTLINE: This is a multicenter study. Patients undergo stem cell mobilization with growth factors alone (filgrastim (G-CSF) and/or sargramostim (GM-CSF)) or chemotherapy followed by growth factors (depending on center). Peripheral blood stem cells (PBSC) are then collected by leukapheresis. Patients then receive high dose chemotherapy consisting of cyclophosphamide IV over 1 hour and cisplatin IV over 72 hours on days -6 to -4 and carmustine IV on day -3 or cyclophosphamide IV, thiotepa IV, and carboplatin IV over 96 hours on days -7 to -4 (depending on center). PBSC are reinfused on day 0. Patients then receive trastuzumab IV over 30-90 minutes weekly for 1 year or until disease progression beginning 5-8 weeks after PBSC reinfusion.