A Phase I/II Study of Frontline Therapy With Polatuzumab Vedotin (Pola) Plus Rituximab (R) in Patients With Post-transplant Lymphoproliferative Disorder (PTLD)

Inclusion Criteria: * Previously untreated biopsy-confirmed CD20-positive monomorphic post-transplant lymphoproliferative disorder (or CD20-positive lymphoma associated with immune deficiency) arising after solid organ or hematopoietic stem cell transplant. This may be defined by either the 2016 World Health Organization classification of lymphoid neoplasms or the 2022 International consensus Classification of Mature Lymphoid Neoplasms or the 2022 World Health Organization classification. * At least 18 years of age. * ECOG performance status ≤ 3. * Adequate hematologic and organ function (unless due to underlying lymphoma per the investigator) as defined below: * Absolute neutrophil count ≥ 1.0 K/cumm * Platelets ≥ 75 K/cumm * Hemoglobin ≥ 8.0 g/dL * Total bilirubin \< 1.5 x IULN * AST(SGOT)/ALT(SGPT) \< 2.5 x IULN * Creatinine clearance \> 30 mL/min measured or by Cockcroft-Gault * Note: Patients with extensive bone marrow involvement by lymphoma and/or disease-related cytopenias may be enrolled if the following criteria are met: * ANC ≥ 0.5 K/cumm * Platelets ≥ 50 K/cumm * Hemoglobin ≥ 7.0 g/dL * The effects of polatuzumab vedotin and rituximab on the developing human fetus are unknown. For this reason, women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a participant become pregnant or suspect pregnancy while participating in this study, the participant must inform the treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document. Exclusion Criteria: * Active central nervous system involvement with lymphoma / PTLD. * Current grade ≥ 2 peripheral neuropathy. * Current ejection fraction \< 40% on transthoracic echocardiogram or multigated acquisition (MUGA) scan * Subjects with history of concurrent second cancers requiring active, ongoing systemic treatment with the following exceptions: * Patients with non-melanoma skin cancer or carcinoma in situ of the cervix will not be excluded. * Patients with previous malignancies are eligible if disease-free for \> 2 years. * Patients on long term hormonal therapy to prevent recurrence of a prior cancer (e.g., hormonal therapy for breast cancer) will not be excluded. * Currently receiving any other investigational agents or received any investigational agents during the 4 weeks prior to the first dose of polatuzumab vedotin. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to polatuzumab vedotin, rituximab, or other agents used in the study. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection (bacterial, fungal, viral, parasitic, or mycobacterial), interstitial lung disease, active non-infectious pneumonitis, congestive heart failure NYHA grade ≥ 3, unstable angina pectoris, or cardiac arrhythmia. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative serum or urine pregnancy test within 7 days prior to C1D1 * Patients with HIV are eligible provided the meet the following criteria: * On antiretroviral regimen and stable on that regimen * Healthy from an HIV perspective * CD4 count \> 250 cells/mcL * Minimal anticipated interactions or overlapping toxicity with polatuzumab vedotin or rituximab * HIV viral load \< 200 copies/mm3 by standard clinical assays * Active hepatitis B infection. * Patients who are hepatitis B surface antigen (HBsAg) negative and hepatitis B core antibody (HBcAb) positive must be negative for hepatitis B virus (HBV) polymerase chain reaction (PCR) to be eligible for study participation. * Active hepatitis C infection. * Patients who are positive for hepatitis C virus (HCV) antibody must be negative for HCV by PCR to be eligible for study participation. * Any serious medical condition or abnormality in clinical laboratory tests that, in the investigator's judgment, precludes the patient's safe participation in and completion of the study, or which could affect compliance with the protocol or interpretation of results.