Safety and Effectiveness of EBV-specific Cytotoxic T Cells for the Treatment for EBV Lymphomas or Other EBV-associated Malignancies

Inclusion Criteria: * A patient will be considered eligible to receive EBV-CTL treatment if the following inclusion criteria are met. Patients should receive established effective therapy if it exists and they can tolerate it prior to enrolling on protocol to receive experimental therapy. Patients will be considered eligible regardless of initial response to rituximab (alloHCT recipients) rituximab and/or multi-agent chemotherapy (SOT and other immune compromised recipients) and appropriate first line chemotherapy (non immune compromised recipients). * Three cohorts of patients will be eligible for enrollment: °Cohort 1 * Patients after allogeneic HCT who have: 1. EBV+ malignancies 2. EBV viremia (as evidenced by two serial plasma EBV DNA assays) without EBV+ malignancy Included in cohort 1 will be patients with underlying immunodeficiency syndromes with: 3\. EBV+ malignancies 4. EBV viremia without current but with a history of prior EBV+ malignancy * Cohort 2 * Patients after allogeneic SOT who have: 1. EBV+ malignancies 2. EBV viremia (as evidenced by two serial plasma EBV DNA assays) without current but with a history of prior EBV+ malignancy. * Patients in Cohort 1 (D) and 2 (B) treated for EBV viremia without evidence of EBV+ malignancy will need to have a history of a prior EBV malignancy with: * Continued viremia at the completion of planned therapy * Recurrence of viremia within 2 months from completion of planned therapy * High grade viremia (\>20,000 copies) after treatment for EBV malignancy * Evidence of EBV positivity for patients in cohort 1 and 2 is determined as follows: * A biopsy showing EBV+ malignancy or * A combination of EBV viremia AND radiographic appearance consistent with an EBV+ malignancy * Cohort 3 A. EBV-associated lymphomas and lymphoproliferative disorders not associated with immunodeficiency (biopsy required) (e.g. EBV+ Hodgkin lymphoma, etc). \- Based on prior studies, patients with NK/T lymphoma will only be eligible for protocol if EBV-CTL therapy is being administered from their HCT donor either prior to or after HCT. B. Other EBV-associated malignancies (biopsy required) including nasopharyngeal carcinoma, EBV+ gastric cancer, EBV+ leiomyosarcoma. * Patients in cohort 3 will be assessed for whether alternative standard therapy is available prior to being consented to the trial. * Patients in cohort 3 will need a biopsy showing EBV+ disease. * Patients in cohort 3 will not be treated for viremia alone. All Patients: 1. Availability of EBV-CTLs generated specifically for the patient and demonstrated to be restricted by a shared HLA-allele. 2. Eastern Cooperative Oncology Group (ECOG) performance status ≤ 3 for patients aged \> 16 years; Lansky score ≥ 20 for patients ≤ 16 years 3. For patients with PTLD in the alloHCT setting, the underlying disease for which alloHCT transplant was performed is either an EBV+ malignancy or in morphologic remission 4. Adequate organ function per the following (unless deemed to be caused by the underlying EBV-driven process which EBV-CTLs are intended to treat, or its prior therapy): A. Absolute neutrophil count ≥ 500/μL, with or without cytokine support B. Platelet count ≥ 20,000/μL, with or without transfusion support C. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 3× the upper limit of normal (ULN) and total bilirubin \< 2.5×ULN; D. Creatinine \< 3×ULN 5. Patient or patient's representative is willing and able to provide written informed consent Exclusion Criteria: 1. Any concomitant investigational therapy that would impair the ability to assess efficacy or toxicity of the EBV-CTL treatment. Simultaneous initiation of rituximab therapy in a patient who has received no prior rituximab. 2. Uncontrolled graft versus host disease or organ rejection or ongoing need for methotrexate, extracorporeal photopheresis, or corticosteroids at a dose greater than 0.5mg/kg/day prednisone or equivalent. 3. Need for vasopressor or ventilatory support, unless deemed to be caused by the EBV-driven process which EBV-CTLs are intended to treat 4. Pregnancy 5. Female of childbearing potential or male with a female partner of childbearing potential unwilling to use a highly effective method of contraception 6. Inability to comply with study procedures 7. Patients who have received allogenic cells from a donor other than their HCT or SOT donor within 30 days.