Genetically Engineered Lymphocyte Therapy After Peripheral Blood Stem Cell Transplant in Treating Patients With High-Risk, Intermediate-Grade, B-cell Non-Hodgkin Lymphoma

Inclusion Criteria: * City of Hope (COH) pathology review confirms that research participant's diagnostic material is consistent with history of intermediate grade B-cell NHL (e.g., diffuse B-cell lymphoma, mantle cell lymphoma, transformed follicular lymphoma) * History of relapse after achieving first remission with primary therapy, or failure to achieve remission with primary therapy * Life expectancy \> 16 weeks * Karnofsky performance scale (KPS) \>= 70% * Negative serum pregnancy test for women of childbearing potential * Research participant has an indication to be considered for autologous stem cell transplantation Exclusion Criteria: * Fails to understand the basic elements of the protocol and/or the risks/benefits of participating in this phase I/II study; evidence of understanding includes passing the Protocol Comprehensive Screening given by the Research Subject Advocate (RSA); a legal guardian may substitute for the research participant * Any standard contraindications to myeloablative HSCT per standard of care practices at COH * Dependence on corticosteroids * Currently enrolled in another investigational therapy protocol * Human immunodeficiency virus (HIV) seropositive based on testing performed within 4 weeks of enrollment * History of allogeneic HSCT or prior autologous HSCT * Active autoimmune disease requiring systemic immunosuppressive therapy * Research participant(s) who are to receive radioimmunotherapy (Zevalin-based)-based conditioning regimens * …