Anti-viral T-cell Therapy by Gamma Capture

Inclusion Criteria: 1. Patient, parent, or legal guardian must have given written informed consent, according to FDA guidelines. For pediatric subject who are developmentally able, assent or affirmation will be obtained, if feasible. 2. Male or female, 1 month through 75 years old, inclusive, at the time of informed consent. 3. Prior allogeneic hematopoietic stem cell transplant (bone marrow, peripheral blood stem cells, single or double cord blood), OR prior solid organ transplant (liver, kidney, lung and/or heart, intestinal, or multivisceral), OR diagnosis of primary immunodeficiency OR current/recent administration of immunosuppressive therapy for cancer or autoimmune disease. 4. Negative pregnancy test for females ≥10 years old or who have reached menarche, unless surgically sterilized. All females of childbearing potential and lactation must agree to use an FDA approved method of birth control for the duration of their participation. 5. Clinical status, at the time of consent, amendable to tapering of steroids to less than 1 mg/kg/day prednisone (or equivalent) prior to cellular infusion. 6. Diagnosis of Adenovirus, CMV, or EBV infection, persistent despite standard therapy. A. Adenovirus Infection or Disease: 1. Active adenovirus infection: (i.e. gastroenteritis, pneumonia, hemorrhagic cystitis, hepatitis, pancreatitis, meningitis) defined as the demonstration of adenovirus by biopsy specimen from affected site(s) (by culture or histology), or the detection of adenovirus by culture, PCR or direct fluorescent antibody stain in fluid in the presence of worsening or persistent clinical or imaging findings despite at least 14 days of appropriate antiviral therapy (i.e. cidofovir, brincidofovir, or other available pharmacological agents) OR 2. Refractory adenoviremia: defined as DNAemia \>5000 copies/mL or \<1 log decrease after at least 2 weeks of appropriate antiviral therapy (i.e. cidofovir, brincidofovir, or other available pharmacological agents) OR 3. Intolerance of or contraindication to antiviral medications. B.CMV Infection or Disease: 1. Active CMV infection: (i.e. pneumonia, meningitis, retinitis, hepatitis, hemorrhagic cystitis, and/or gastroenteritis) defined as the demonstration of CMV by biopsy specimen from affected site(s) (by culture or histology) or the detection of CMV by culture, PCR or direct fluorescent antibody stain in fluid in the presence of worsening or persistent clinical or imaging findings despite at least 14 days of appropriate antiviral therapy (i.e. Foscarnet, ganciclovir, cidofovir, or other available pharmacological agents) OR 2. Refractory CMV viremia: defined as the continued presence of DNAemia, with ≥2,000 IU/mL or \<1 log decrease after at least 14 days of appropriate antiviral therapy (i.e. Foscarnet, ganciclovir, cidofovir, or other available pharmacological agents) OR 3. Intolerance of or contraindication to antiviral medications. C. EBV Infection or Disease: 1. Biopsy proven lymphoma or posttransplant lymphoproliferative disease with EBV genomes detected in tumor cells by immunocytochemistry (i.e. EBER positive) or in situ PCR, OR 2. Clinical or imaging findings consistent with EBV lymphoma and associated elevated EBV viral load in peripheral blood in a patient where biopsy is deemed too high risk, OR 3. Failure of antiviral therapy, as determined by one of the two bullets below after three weeks of anti-CD20 targeted therapy such as Rituximab. i. There was an increase or less than 50% response at sites of lymphoma disease or lymphoproliferation. ii. There was a rise or a fall of less than 50% in EBV viral load in peripheral blood of PTLD patients. Exclusion Criteria: 1. Received Antithymocyte Globulin (ATG) or Alemtuzumab within 28 days of viral-specific T cell infusion and a lack of evidence of T cell survival, defined by \<10 CD3+ T cells/uL (in unique situations, plasmapheresis may be considered). 2. Active acute GVHD grades II-IV. 3. Received donor lymphocyte infusion, with the exception of a fraction of an umbilical cord blood, within 14 days of viral-specific T cell infusion. Subjects receiving a fraction of an umbilical cord blood within 14 days of the viral-specific T cell infusion will not be excluded. 4. Active and uncontrolled relapse of malignancy (other than EBV+ post-transplant lymphoproliferative disorder or lymphoma). 5. Received an investigational product in the preceding 2 weeks (prior to infusion) that may impact Viral Specific T-cells (VST) survival. 6. Females of child bearing potential must not be lactating. 7. Past or current medical problems or findings from physical examination or laboratory testing that are not listed above, which, in the opinion of the investigator, may pose additional risks to participation in the study, may interfere with the participant's ability to comply with study requirements, or that may impact the quality or interpretation of the data obtained from the study.