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 dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy * Platelets \>= 50 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 dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy * Creatinine clearance (mL/min) \>= 30 mL/min (obtained within 14 days prior to initiating study treatment) * Cockcroft-Gault Equation * 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 dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy * Bilirubin =\< 3.0 x upper limit of normal (ULN). Subjects with Gilbert's syndrome may be enrolled despite a total bilirubin level \> 3.0 mg/dL if their conjugated bilirubin is =\< 3.0 x ULN) (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 dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy * Aspartate aminotransferase (AST) =\< 3.0 x ULN (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 dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy * Alanine aminotransferase (ALT) =\< 3.0 x ULN (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 dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy * Females of childbearing potential must have a negative serum pregnancy test within 3 days prior to registration. NOTE: Females are considered of childbearing potential unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or they are naturally postmenopausal for at least 12 consecutive months. Documentation of postmenopausal status must be provided * Females of childbearing potential must be willing to abstain from heterosexual activity or to use 2 forms of effective methods of contraception from the time of informed consent until 12 months after treatment the last dose of rituximab or tafasitamab. The two contraception methods can be comprised of two barrier methods, or a barrier method plus a hormonal method or an intrauterine device that meets \< 1% failure rate for protection from pregnancy in the product label * Male subjects with female partners must have had a prior vasectomy or agree to use an adequate method of contraception (i.e., double barrier method: condom plus spermicidal agent) starting with the first dose of study therapy through 12 months after the last dose of rituximab * Subjects with prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the experimental regimen are eligible for the trial * Subject is willing and able to comply with study procedures based on the judgement of the investigator or protocol designee Exclusion Criteria: * Uncontrolled active infection. Patients requiring systemic therapy are eligible if the infection is deemed controlled by the investigator * Post-transplant lymphoproliferative disorder following liquid transplantation * Pregnant or breastfeeding (NOTE: breast milk cannot be stored for future use while the mother is being treated on study and lactating females must agree to not breastfeed while taking study drugs) * Subjects with central nervous system (CNS) involvement by PTLD * Uncontrolled concomitant illness including, but not limited to, symptomatic congestive heart failure (New York Heart Association \[NYHA\] class III or IV), unstable angina pectoris, myocardial infarction within 1 month prior to enrollment, uncontrolled cardiac arrhythmias, uncontrolled seizures, or severe non-compensated hypertension (systolic blood pressure \>= 180 mmHg or diastolic blood pressure \>= 120 mmHg) * History of progressive multifocal leukoencephalopathy * Active hepatitis B infection with positive viral polymerase chain reaction (PCR) from the blood. Subjects with active hepatitis B infection and undetectable viral PCR from the blood will be allowed with concurrent use of entecavir suppression * Prior treatment for PTLD with the exception of radiation, antivirals, steroids and reduced immunosuppression * Electrocardiogram (ECG) abnormality at screening has to be documented by the investigator as not medically relevant * Any condition, including the presence of laboratory values which is deemed by the clinician to place the subject at an unacceptable risk or confounds the ability to interpret the data from this study * Live virus vaccines must not be administered within 28 days of the start of study treatment * Any investigational treatments must have been completed at least 7 days prior to the start of study treatment