TETRAVI Multivirus CTL for Treatment of EBV, CMV, Adenovirus, and BK Infections Post Allogeneic SCT.

Inclusion Criteria: 1. Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells or single or double cord blood. Or Received CAR-T cells targeting an antigen expressed on normal virus specific T cells 2. Treatment for Infection/Disease will fall into one of 3 categories (options): * Option 1: Persistent, increasing or recurrent infections despite 7 days of standard therapy; * a. CMV: Treatment of persistent or relapsed CMV disease or infection after standard therapy. For CMV infection, standard therapy is defined as antiviral therapy with ganciclovir, foscarnet, letermovir or cidofovir. 56, 57 * i. CMV disease: defined as the demonstration of CMV by biopsy specimen from visceral sites (by culture or histology) or the detection of CMV by culture or direct fluorescent antibody stain in broncheoalveolar lavage fluid in the presence of new or changing pulmonary infiltrates or changes consistent with CMV retinitis on ophthalmologic examination. * ii. CMV infection: defined as the presence of CMV positivity as detected by PCR or pp65 antigenemia or culture from ONE site such as stool or blood or urine or nasopharynx or bronchoalveolar lavage. * b. Adenovirus: Treatment of persistent adenovirus infection or disease despite standard therapy. Standard therapy is defined as antiviral therapy with cidofovir. * i. Adenovirus infection: defined as the presence of adenoviral positivity as detected by PCR or culture from ONE site such as stool or blood or urine or lung or nasopharynx. * ii. Adenovirus disease: defined as the presence of adenoviral positivity as detected by PCR, DFA or culture from two or more sites such as stool or blood or urine or lung or nasopharynx. * c. EBV: For treatment of persistent EBV infection despite standard therapy. For EBV infection, standard therapy is defined as rituximab given at 375mg/m2 in patients for 1-4 doses with a CD20+ve tumor.58 * i. EBV infection: defined as: (1) Biopsy proven lymphoma with EBV genomes detected in tumor cells by immunocytochemistry or in situ PCR; * ii. (2) Or clinical or imaging findings consistent with EBV lymphoma and/or elevated EBV viral load in peripheral blood. * d. BK virus: Treatment of persistent BK virus infection or BK virus disease despite antiviral treatment with cidofovir or leflunomide. No clear standard treatment is defined (section 1.1.5). Cidofovir has been administered in low doses as well as high doses to HSCT patients with BK infections but no randomized trials are available proving its clinical efficacy. * i. BK virus infection is defined as the presence of BK virus positivity as detected by PCR or culture in one site such as blood or urine or lung. * ii. BK virus disease is defined as the presence of BK virus detectable by culture or PCR in blood or urine or other body fluids or lungs and symptoms of disease including, but not limited to persistent microscopic or macroscopic hematuria or detectable BK virus in more than one site. * e. JC virus: Treatment of JC virus infection or disease without suitable alternative treatment option. Given the high homology (\>90%) between JC and BK and the fact that BKVSTs targeting VP1 and Large T (as targeted in our multivirus MVSTs) have been administered to treat JCV-PML, and produced viral clearance from the cerebrospinal fluid, it is likely that our MVSTs will have efficacy against JC virus. Given the current lack of treatment options for JC virus infection or reactivation after HSCT and the risk of progression to JML, which is almost uniformly fatal, and the apparent activity of BK virus- directed T cells against JC virus infected cells, we propose including patients with JC virus on this study, unless a suitable alternative therapy is available. * i. JC virus infection is defined as the presence of elevated JC virus levels as detected by PCR or positive culture in one site such as CSF or blood. * ii. JC virus disease is defined as defined as the presence of JC virus detectable by culture or PCR in one or more sites such as blood or CSF and symptoms of disease including symptoms of PML OR detectable JC virus by PCR or culture in more than one site. * Option 2: Early treatment for single or multiple infections with EBV, CMV, adenovirus, and/or BK virus will be allowed for patients deemed to be unable to tolerate standard therapy. Patients with multiple CMV, EBV, Adenovirus, and BK virus infections are eligible given that at least one infection is persistent despite standard therapy as defined above. Patients with multiple infections or reactivations are eligible to enroll. * Option 3: For patients having adenovirus and BK virus, the requirement to fail one week of standard therapy would be waived if they meet one of the criteria below: 1. They are ≤100 days post- transplant 2. They are currently receiving other nephrotoxic agents or marrow-suppressive agents 3. They have adenovirus copy number ≥10,000 copies/ml 3. Clinical status at enrollment to allow tapering of steroids to equal or less than 0.5 mg/kg/day methylprednisolone (or equivalent). 4. Hgb ≥ 7.0 gm/dl 5. Available MVSTs must be partially HLA matched with recipient and HLA match must be verified by one of the Principal Investigators. 6. Negative pregnancy test in female patients if applicable (childbearing potential who have received a reduced intensity conditioning regimen). 7. Written informed consent and/or signed assent line from patient, parent or guardian. Exclusion Criteria 1. Patients receiving ATG, Campath or other immunosuppressive T cell monoclonal antibodies within 28 days of screening for enrollment. 2. Patients with other uncontrolled infections. For bacterial infections, patients must be receiving definitive therapy and have no signs of progressing infection for 72 hours prior to enrollment. For fungal infections patients must be receiving definitive systemic anti-fungal therapy and have no signs of progressing infection for 1 week prior to enrollment. Progressing infection is defined as hemodynamic instability attributable to sepsis or new symptoms, worsening physical signs or radiographic findings attributable to infection. Persisting fever without other signs or symptoms will not be interpreted as progressing infection. 3. Patients who are less than 28 days removed from their allogeneic hematopoietic stem cell transplant or who have received donor lymphocyte infusions (DLI) or CAR-T within 28 days. 4. Patients with active acute GVHD grades II-IV. 5. Uncontrolled relapse of malignancy 6. Requirement for FiO2 \> 50% oxygen to maintain oxygen saturation \> 90% (peripheral pulse-ox). Note: patients requiring oxygen at FiO2\<=50% to maintain arterial oxygen saturation \>90% are eligible to receive MVSTs if the reason for this oxygen requirement is believed attributable to the virus being treated.