Combination Chemotherapy Followed By Autologous Stem Cell Transplant, and White Blood Cell Infusions in Treating Patients With Non-Hodgkin's Lymphoma

OBJECTIVES: * Determine the toxicity of high-dose combination chemotherapy comprising cyclophosphamide, thiotepa, and carboplatin followed by autologous peripheral blood stem cell transplantation and immunotherapy consolidation therapy comprising anti-CD3 x anti-CD20 bispecific antibody (CD20Bi)-activated T cells (ATC) in patients with non-Hodgkin's lymphoma. * Determine the maximum tolerated dose of CD20Bi-ATC in patients treated with this regimen. * Determine whether ATC traffic to tumor sites in select patients treated with this regimen. * Assess the immune reconstitution of B cells and incidence of infection in patients treated with this regimen. * Compare relapse rates and overall survival of patients treated with this regimen with historical controls. OUTLINE: This is a dose-escalation study of activated T cells. * Peripheral blood stem cell (PBSC) mobilization and collection: Patients receive filgrastim (G-CSF) subcutaneously (SC) once daily for 5 days. They then undergo leukaphereses to collect peripheral blood stem cells (PBSC). Some of the lymphocytes are treated in the laboratory to produce anti-CD3 x anti-CD20 bispecific antibody (CD20Bi)-activated T cells (ATC). * High-dose chemotherapy and PBSC transplantation: Patients receive carmustine IV on day -7, etoposide IV twice daily and cytarabine IV twice daily on days -6, -5, -4, and -3, and melphalan IV on day -2. Autologous PBSC are reinfused on day 0. * Immunotherapy consolidation: Patients receive immunotherapy consolidation comprising CD20Bi-ATC IV over 15-30 minutes starting on day 4, once a week for 4 weeks for a total of four infusions. Cohorts of 3-6 patients receive escalating doses of CD20Bi-ATC until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 2 of 3 or 2 of 6 patients experience dose-limiting toxicity. After completion of study treatment, patients are followed periodically for survival. PROJECTED ACCRUAL: A total of 12-24 patients will be accrued for this study.