An Open-Label, Single Center Phase 2 Study of Magrolimab, Rituximab and Radiation as Bridging Strategy Before CAR T-Cell Therapy in Patients With Relapsed or Refractory Large B-cell Lymphoma

Inclusion Criteria: Eligible subjects will be considered for inclusion in this study if they meet the following criteria based on tests obtained less than 4 weeks from first dose: 1. Relapsed or refractory DLBCL, PMBCL, tFL, or HGBCL, at least 1 prior line of systemic therapy 2. Planned to receive standard of care therapy with axi-cel, tisa-cel or liso-cel 3. ≥ 18 years of age because no dosing or adverse event data are currently available on the use of magrolimab in combination with rituximab and radiation in patients \<18 years of age, children are excluded from this study. 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 5. Measurable nodal disease of ≥ 1.5 cm, extra-nodal disease \> 1 cm, or splenomegaly \> 12 cm, deemed appropriate for radiation 6. At least two weeks or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic therapy at the time the subject is planned for leukapheresis, except for systemic immune checkpoint inhibitory/immune stimulatory therapy. At least 3 half-lives must have elapsed from any prior systemic immune checkpoint inhibitory/immune stimulatory therapy at the time the subject is planned for leukapheresis 7. Toxicities due to prior systemic and local therapy must be stable and recovered to ≤ Grade 1 (except for clinically non-significant toxicities such as alopecia) 8. Absolute neutrophil count of ≥ 1.0×109/L, with no G-CSF support for 1 week 9. Platelet count of ≥ 50×109/L and hemoglobin \> 9 g/dL without transfusion for 7 days prior to screening assessment 10. Creatinine clearance (as estimated by Cockcroft Gault) ≥ 30 mL/min 11. Serum alanine transaminase (ALT) / aspartate transaminase (AST) ≤ 2.5 upper limit of normal (ULN) 12. Total bilirubin ≤1.5 mg/dL, except in subjects with Gilbert's syndrome. 13. Cardiac ejection fraction ≥ 45% with no evidence of clinically significant pericardial effusion 14. Baseline oxygen saturation \> 92% on room air 15. No evidence of active lymphoma involving the central nervous system (CNS) at time of screening per investigator clinical assessment 16. Females of childbearing potential must have a negative serum or urine pregnancy test (females who have undergone surgical sterilization or who have been postmenopausal for at least 2 years are not considered to be of childbearing potential) 17. Patient will be willing to undergo a tissue biopsy during the screening period , before initiation of lymphodepleting chemotherapy, and at time of progression prior to initiation of next line of therapy; archived samples can be accepted during the screening period in absence of intercurrent treatment 18. Due to the risk of developing anemia, and because magrolimab may make phenotyping difficult, ABO/Rh type, antibody screen, blood phenotyping or genotyping, and DAT need to be performed at screening before exposure to magrolimab 19. The effects of magrolimab, rituximab and radiation on the developing human fetus are unknown. For this reason and because chemotherapy and radiotherapy agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and and for up to 6 months after the administration of magrolimab, rituximab, and/or radiation (whichever is administered last). (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following: * Postmenopausal (no menses in greater than or equal to 12 consecutive months). * History of hysterectomy or bilateral salpingo-oophorectomy. * Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy). * History of bilateral tubal ligation or another surgical sterilization procedure. * Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 6 months after completion of magrolimab, rituximab and radiation administration. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: Subjects will be ineligible for this study if they meet the following criteria: 1. History of malignancy other than nonmelanoma skin cancer or localized carcinoma (e.g. cervix, bladder, breast, prostate) unless disease free for at least 3 years. 2. History of Richter's transformation of chronic lymphocytic leukemia (CLL) 3. Autologous stem cell transplantation within 6 weeks of planned CART infusion 4. History of allogeneic stem cell transplantation within 12 weeks of planned CART infusion 5. Has any condition that requires systemic treatment with corticosteroids, prednisone equivalents, or other immunosuppressive medications within 28 days prior to first dose of study drug (inhaled or topical; corticosteroids; pre-medication for treatment; short course not to exceed 5 days; or brief course of steroids given for prophylaxis of contrast dye allergic response are permitted). 6. Known presence of fungal, bacterial, viral, or other infection that is uncontrolled or requiring IV antimicrobials for management. Simple UTI and uncomplicated bacterial pharyngitis are permitted if responding to active treatment and after consultation with the Principal investigator. 7. Known history of infection with HIV or hepatitis B (HBsAg positive) or hepatitis C virus (anti-HCV positive). A history of HIV, hepatitis B or hepatitis C is permitted if the viral load is undetectable per quantitative PCR and/or nucleic acid testing. For subjects with a history of Hepatitis B or C, standard of care monitoring for viral reactivation will be conducted. Subjects with a history of Hepatitis B will be required to undergo hepatitis B reactivation prophylaxis unless contraindicated. 8. Subjects with known detectable cerebrospinal fluid malignant cells or known active brain malignant lesions 9. History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or other clinically significant cardiac disease within 6 months of enrollment 10. History of primary immunodeficiency 11. History of autoimmune disease (e.g. Crohns, rheumatoid arthritis, systemic lupus) resulting in end organ injury or requiring systemic immunosuppression/systemic disease modifying agents within the last year considered significant in the opinion of the principal investigator 12. History of symptomatic deep vein thrombosis or symptomatic pulmonary embolism within 6 months of enrolment considered significant in the opinion of the principal investigator 13. Any medical condition likely to interfere with assessment of safety or efficacy of study treatment in the investigator's opinion 14. History of severe immediate hypersensitivity reaction to any of the agents used in this study, including E coli-derived proteins. Regarding rituximab, exclusion is for known severe anaphylaxis to rituximab or any allergic reaction to rituximab that in the opinion of the PI and treating physician contraindicate re-challenge with rituximab 15. Live vaccine ≤ 6 weeks prior to planned start of conditioning regimen 16. Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the preparative chemotherapy on the fetus or infant. 17. Women of child-bearing potential and men with partners who are of child-bearing potential who are not willing to practice birth control as noted in section 4.1 from the time of consent through 6 months after the completion of magrolimab, rituximab, and/or radiation therapy (whichever is administered last). 18. In the investigator's judgment, the subject is unlikely to complete all protocol-required study visits or procedures, including follow-up visits, or comply with the study requirements for participationTrial Treatments 19. Prior exposure to CD47/SIRPα antagonist/inhibitor, independent of indication 20. History of uncontrolled autoimmune hemolytic anemia (AIHA) or idiopathic thrombocytopenic purpura (ITP). 21. History of hemolytic transfusion reaction secondary to allo-antibodies. 22. Patients for whom radiation therapy cannot be performed safely