3 courses of early intensification: First course: Ifosfamide (IFF) IV continuously and Etoposide (VP-16) IV over 2 hours every 12 hours on days 1-3. Filgrastim (G-CSF) administered subcutaneously (SC) beginning on day 5 and continuing until blood counts recover then autologous peripheral blood stem cells (PBSC) are harvested, selected for CD34 positive cells, and purged in vitro. If more than 5% of the WBC contains lymphoma cells after induction, then 2 courses of IFF and VP-16 are administered before PBSC harvest. Second course: IFF IV continuously on days 1-3, mitoxantrone (DHAD) IV on day 1, and G-CSF SC as in first course. Third course: Carmustine IV over 1 hour on day -6, ARA-C and VP-16 IV every 12 hours on days -5 to -2, and melphalan IV on day -1. PBSC are reinfused on day 0. G-CSF is administered SC beginning on day 0 and continuing until blood counts recover. Each course lasts 3 weeks in the absence of disease progression or unacceptable toxicity.