Antiviral Cellular Therapy for Enhancing T-cell Reconstitution Before or After Hematopoietic Stem Cell Transplantation

Inclusion Criteria Patients who have received any type of allogeneic transplant or who have a primary immunodeficiency disorder will be eligible if they have CMV, adenovirus, and/or EBV infection/disease with failure of treatment after 7 days of standard therapy OR if unable to tolerate standard therapy. * Patients must meet one of the following criteria: * Recipient of prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cell or single or double cord blood within the previous 18 months, OR * Have a diagnosed primary immunodeficiency disorder (as defined by clinical and laboratory evaluations) and not undergone HSCT. * Treatment of the following persistent or relapsed infections despite standard therapy: * 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 or cidofovir for at least 14 days. * Adenovirus: Treatment of persistent or relapsed adenovirus infection or disease despite standard therapy. Standard therapy is defined as antiviral therapy with cidofovir or brincidofovir. * EBV: Treatment of persistent or relapsed EBV infection despite standard therapy. For EBV infection, standard therapy is defined as rituximab given at 375 mg/m2 in patients for 1-4 doses with a CD20+ tumor. Additional Inclusion Criteria: * Patients with simultaneous infe…