FT596 With Rituximab as Relapse Prevention After Autologous HSCT for NHL

Inclusion Criteria: * Diagnosis of diffuse large B cell lymphoma or aggressive (high-grade) B-cell lymphoma for which an autologous stem cell transplant is planned or recently completed * High risk for relapse defined as at least one of the below: * Primary induction failure (no complete or partial remission at any point after diagnosis * Initial remission duration \< 12 months * Lack of complete metabolic (PET scan) response after 2-3 cycles of salvage chemotherapy * Evidence of c-myc and bcl-2 and/or bcl-6 re-arrangement (double hit or triple hit lymphoma) * Age-adjusted IPI 2-3 at relapse * Age 18 years or older at the time of signing consent. * Agrees to use adequate contraception (or evidence of sterility) for at least 12 months after the last dose of rituximab. * Agrees and signs the separate consent for up to 15 years of follow-up (Long-term Follow-up study CPRC#2020LS052) * Provides voluntary written consent prior to the performance of any research related activities. Exclusion Criteria: * Receipt of any investigational therapy within 28 days prior to the first dose of FT596 or planned use of an investigational therapy during the first 100 days after transplant * Planned post-transplant irradiation prior to Day +100 * Seropositive for HIV, active Hepatitis B or C infection with detectable viral load by PCR * Body weight \<50kg * Known allergy to the following FT596 components: albumin (human) or DMSO * Unable to receive rituximab Post-HSCT Reconfirmation of eligibility * No life-threatening medical issues (i.e. ongoing Grade 4 adverse events) where, in the opinion of the treating investigator, use of FT596 is not in the patient's best interest. * No active uncontrolled infection. * Adequate organ function post-transplant including: * alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤5 x ULN (Grade 2 CTCAE v5) * total bilirubin ≤1.5 x ULN (Grade 1 CTCAE v5) * serum creatinine ≤1.5 x ULN (Grade 1 CTCAE v5) * oxygen saturation ≥93% on room air * For Day 30 dosing only - CBC requirement consistent with engraftment (ANC\>500, platelet\>20,000 without transfusion support within previous 7 days). There are no CBC parameters for Day 7 dosing. * No requirement for systemic immunosuppressive therapy (\> 5mg prednisone daily) during the FT596 dosing period.