Allogeneic Virus-Specific Cytotoxic T-Lymphocytes(CTL), Persistent/Recurrent Viral Infection Post-HSCT (EAP CHALLAH)

Inclusion Criteria: 1. Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow, peripheral blood stem cells or single or double umbilical cord blood. 2. CMV, adenovirus or EBV infection persistent despite standard therapy 1. For CMV infection * Patients with 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 bronchoalveolar lavage fluid in the presence of new or changing pulmonary infiltrates OR * Failure of antiviral therapy: defined as the continued presence of pp65 antigenemia (\>1+ cell/100,000 cells) or DNAemia (as defined by reference lab performing PCR assay but usually \>400 copies/ml) after at least 7 days of antiviral therapy OR * Relapse after antiviral therapy defined as recurrence of either pp65 antigenemia or DNAemia after at least 2 weeks of antiviral therapy * For CMV infection, standard therapy is defined as 7 days therapy with Ganciclovir, Foscarnet or Cidofovir for patients with disease or recurrence after 14 days therapy 2. For EBV infection * EBV infection is defined as: * Biopsy proven lymphoma with EBV genomes detected in tumor cells by immunocytochemistry or in situ PCR OR * Or clinical or imaging findings consistent with EBV lymphoma and elevated EBV viral load in peripheral blood. * For EBV infection, standard therapy is defined as rituximab given at 375mg/m2 in patients for 1-4 doses with a CD20+ve tumor * Failure is defined as * There was an increase or less than 50% response at sites of disease for EBV lymphoma OR * There was a rise or a fall of less than 50% in EBV viral load in peripheral blood or any site of disease 3. For adenovirus infection or disease * Adenovirus infection is defined as the presence of adenoviral positivity as detected by PCR, DAA or culture from ONE site such as stool or blood or urine or nasopharynx OR * Adenovirus disease will be defined as the presence of adenoviral positivity as detected by culture from two or more sites such as stool or blood or urine or nasopharynx * Standard therapy is defined as 7 days therapy with Cidofovir (if renal function permits this agent to be given). * Failure is defined as a rise or a fall of less than 50% in viral load in peripheral blood or any site of disease as measured by PCR or any other quantitative assay). 3. Patients with multiple CMV, EBV or Adenovirus infections are eligible given that each infection is persistent despite standard therapy as defined above. Patients with multiple infections with one persistent infection and one controlled infection are eligible to enroll. 4. Clinical status at enrollment to allow tapering of steroids to less than 0.5 mg/kg/day prednisone. 5. Written informed consent and/or signed assent line from patient, parent or guardian. Exclusion Criteria: 1. Received ATG, or Campath or other immunosuppressive T cell monoclonal antibodies within 28 days of screening for enrollment. 2. 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. 3. 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. 4. Received donor lymphocyte infusion (DLI) within 28 days. 5. Active acute GVHD grades II-IV. 6. Active and uncontrolled relapse of malignancy 7. Pregnant or lactating in female patients, if applicable (childbearing potential who have received a reduced intensity conditioning regimen).