Inclusion Criteria:  Patients > or = 18 years of age or older. For BKV, ADV or CMV infections: Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using bone marrow, peripheral blood stem cells or single or double umbilical cord blood. For JC virus and COVID19 infection: no prior hematopoietic stem cell transplantation (HSCT) is required. For BKV infection, patients need to have polymerase chain reaction (PCR) positive for BKV (in peripheral blood or urine) with consistent clinical symptoms. For ADV infection, patients need to have PCR positive for ADV in peripheral blood AND/OR patients need to fit criteria of probable or definitive adenovirus organ disease. For CMV infection, patients need to have PCR positive for CMV in peripheral blood AND/OR patients need to fit criteria of probable or definitive CMV disease. For JCV, patients need to have documented JC viral encephalitis or JC end-organ disease. For COVID-19 infection, patients need to have COVID-19 related pneumonia/acute respiratory distress syndrome (ARDS) to be enrolled, defined as patients with a positive COVID-19 test (bronchoalveolar lavage [BAL], nasal or pharyngeal) and radiological and clinical signs of pneumonia or ARDS. Written informed consent from patient or designated power of attorney. Subjects are also are required to consent to PA17-0483 for long term follow up per the guidelines set forth by the Food and Drug Administrations' (FDA's) Biologic Response Modifiers Advisory Committee (BRMAC). Negative pregnancy blood test in female patients of childbearing potential, defined as not post-menopausal for 12 months or no previous surgical sterilization. Women of child bearing potential must be willing to use at least two forms of birth control during the study and for at least 6 months after stopping treatment. Acceptable forms of birth control include intrauterine device (IUD), hormonal methods (birth control pills, injections, and implants), condoms, diaphragms, tubal ligation, or vasectomy.  Exclusion Criteria:  Patients who have received anti-thymocyte globulin (ATG) within 14 days or have received donor lymphocyte infusion (DLI) or campath within 28 days of enrollment. Patients with other uncontrolled infections (excluding human immunodeficiency virus [HIV]/acquired immunodeficiency syndrome [AIDS]). For bacterial infections, patients must be receiving definitive therapy and have signs of improving infection prior to enrollment as determined by the principal investigator (PI). For fungal infections, patients must be receiving definitive systemic anti-fungal therapy and have signs of improving infection prior to enrollment as determined by the PI. Patients with active steroid refractory graft versus host disease (GVHD). Patients on immunosuppressive therapy other than tacrolimus, sirolimus or steroids Active and uncontrolled relapse of malignancy. Patients with controlled malignancy on maintenance therapy would be eligible for the study.