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

Inclusion Criteria: * Diagnosis of either mycosis fungoides (MF) or Sezary syndrome (SS) by the World Health Organization (WHO) 2016 classification (Swerdlow et al., 2017), stage IB-IV by modified International Society for Cutaneous Lymphomas (ISCL)/ European Organization of Research and Treatment of Cancer (EORTC) classification (Olsen et al., 2011), without large cell transformation (LCT) at the time of screening. Patients with a history of prior LCT are permitted * Patients must have had at least one prior course of systemic therapy * Age \>= 18 years * Because no dosing or adverse event data are currently available on the use of Hu5F9-G4 (magrolimab) in combination with mogamulizumab in patients \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Hemoglobin \>= 9.5 g/dL and transfusion independence (defined as not requiring more than 2 units of red blood cell \[RBC\] transfusions during the 4-week period prior to screening) * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 75,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) except for subjects with Gilbert's syndrome or genetic equivalent * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN * Glomerula…