Memory Enriched T Cells Following Stem Cell Transplant in Treating Patients With Recurrent B-Cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Research participants enrolled are patients with an indication to be considered for HSCT, who are diagnosed with intermediate or high grade B-cell non-Hodgkin lymphoma (NHL) (e.g. diffuse large B-cell lymphoma \[DLBCL\], mantle cell lymphoma \[MCL\], or transformed NHL), and that have either (1) recurrence/progression following prior therapy, or (2) verification of high-risk disease in first or subsequent remission * Karnofsky performance status (KPS) of \>= 70% at time of enrollment * Life expectancy \>= 16 weeks at time of enrollment * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately * City of Hope (COH) pathology review confirms that research participant's diagnostic material is consistent with history of intermediate or high grade B-cell NHL (e.g., DLBCL, MCL, or transformed NHL) * Negative serum pregnancy test for women of child-bearing potential * Research participant has an indication to be considered for autologous stem cell transplantation * All subjects must have the ability to understand and the willingness to sign a written informed consent ELIGIBILITY CRITERIA AT TIME OF INFUSION OF GENETICALLY MODIFIED AUTOLOGOUS T CEL…