Tafasitamab and Rituximab for Front-Line Treatment of Post-Transplant Lymphoproliferative Disorder

Inclusion Criteria: * Written informed consent obtained to participate in the study and Health Insurance Portability and Accountability Act (HIPAA) authorization for release of personal health information * Age \>= 18 years at the time of consent * Karnofsky scale \> 30% or Eastern Cooperative Oncology Group (ECOG) =\< 3 (can be assessed after pre-phase steroids) * Histological evidence of B-cell PTLD (monomorphic and polymorphic) following solid organ transplantation; expresses CD19 and CD20, with or without EBV association, confirmed after biopsy or resection of tumor * Measurable disease of \> 1.5 cm in diameter and/or bone marrow involvement * Subjects having undergone heart, lung, liver, kidney, pancreas, small intestine transplantation or a combination of the organ transplantations mentioned * No prior lines of therapy for PTLD (palliative radiation, steroids, antiviral therapy, and reduction in immunosuppression are allowed) * Human immunodeficiency virus (HIV) infection is allowed if viral load is undetectable at time of enrollment and CD4+ count \> 200 cells/uL * Expected survival greater than 30 days * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L (obtained within 14 days prior to initiating study treatment) * Note: Hematology and other lab parameters that are =\< grade 2 BUT still meet criteria for study entry are allowed. Furthermore, changes in laboratory parameters during the study should not be considered adverse events unless they meet criteria for dos…