Testing the Addition of an Anti-cancer Drug, Hu5F9-G4 (Magrolimab), to the Usual Chemotherapy Treatment (Mogamulizumab) in T-Cell (a Type of Immune Cell) Lymphoma That Has Returned After Treatment or Does Not Respond to Treatment

PRIMARY OBJECTIVES: I. To characterize the safety and toxicity profile and to determine a safe recommended phase 2 dose (RP2D) of Hu5F9-G4 (magrolimab) when given in combination with mogamulizumab. (Phase I) II. To compare the proportion of patients who achieve a partial or complete response lasting at least 6 months (ORR6) of the combination of Hu5F9-G4 (magrolimab) and mogamulizumab versus mogamulizumab alone. (Phase II) SECONDARY OBJECTIVES: I. To observe and record anti-tumor activity. (Phase I) II. To compare the efficacy of the combination of Hu5F9-G4 (magrolimab) and mogamulizumab versus mogamulizumab alone with respect to the following endpoints (Phase II): IIa. Overall response rate (ORR); overall response rate lasting at least 4 months (ORR4); overall response rate lasting at least 12 months (ORR12). IIb. Duration of response (DOR). IIc. Progression-free survival (PFS). IId. Time to next treatment (TTNT). EXPLORATORY OBJECTIVES: I. To identify potential biomarkers that correlate with response to mogamulizumab and Hu5F9-G4 (magrolimab) including (Phase I and II): Ia. Expression of CCR4. Ib. Somatic mutations and germline polymorphisms. Ic. Phenotyping of lymphoma and immune microenvironment. Id. Functional assay of phagocytosis. OUTLINE: This is a phase Ib, dose de-escalation study of magrolimab followed by a phase II study. Patients in the phase Ib study receive treatment as in Arm I. Patients in the phase II study are randomized to Arm I or Arm II. ARM I: Patients receive magrolimab intravenously (IV) over 2-3 hours weekly during cycles 1-2, then every 2 weeks (Q2W) during cycles 3-12. Patients also receive mogamulizumab IV over at least 60 minutes weekly during cycle 1, then Q2W during cycles 2-12. Cycles repeat every 28 days for up to 12 cycles in the absence of disease progression or unacceptable toxicity. Patients undergo positron emission tomography (PET)/computed tomography (CT) or diagnostic CT, blood sample collection, and may undergo a skin punch biopsy during screening and on study. ARM II: Patients receive mogamulizumab IV over at least 60 minutes weekly during cycle 1, then Q2W during cycles 2-12. Cycles repeat every 28 days for up to 12 cycles in the absence of disease progression or unacceptable toxicity. Patients who have received at least 2 full treatment cycles and have progressive disease (PD) or have received at least 6 full treatment cycles and have stable disease (SD) may crossover to Arm I. Patients undergo PET/CT or diagnostic CT, blood sample collection, and may undergo a skin punch biopsy during screening and on study. After completion of study treatment, patients are followed up every 3 months for 2 years.