Cytotoxic T Lymphocytes in Treating Patients With Malignancies With BK and/or JC Virus

Inclusion Criteria: * Patients ≥ 2 years. * English and non-English speaking patients are eligible. * Immunocompromised patients including but not limited to those with any type of malignancy, HIV/AIDS, or history of solid organ transplant * Non-immunocompromised patients with PML/JC virus encephalitis * Microscopic or greater hematuria urine or blood PCR positive for BK virus * Biopsy proven BK nephritis and urine or blood PCR positive for BK virus disease and/or polyomavirus. * Definite or probable PML/JC viral encephalitis (see Appendix C) * JC end-organ disease * Receiving \> 6 mg / day of prednisone or equivalent at the time of enrollment. * Patients with BK virus hemorrhagic cystitis, who are receiving treatment with cidofovir, leflunomide, or other antiviral therapy with no response, will be eligible for CTL infusion. * Patients with JCV encephalitis / PML may be receiving pembrolizumab. * Written informed consent and/or signed assent from patient, parent or guardian. * Patients with cognitive impairments are eligible. * A negative pregnancy test in female patients of childbearing potential. Childbearing potential is defined as pre-menopausal, post-menopausal for \< 1 year, and not having undergone surgical sterilization. * Women of childbearing potential must be willing to use an effective contraceptive measure while on study. * Patients enrolled on this study may be enrolled on other IND studies at the discretion of the PI. * Patients with bacterial infections must be receiving definitive therapy and have no signs of progressing infection for 72 hours prior to enrollment. * Patients with fungal infections patients must be receiving definitive systemic anti fungal therapy and have no signs of progressing infection for 1 week prior to enrollment. * Patients may be re-enrolled in the protocol if the BK or JC virus infection recurs, so long as they meet all the other eligibility criteria at the time of re-enrollment. Exclusion Criteria: * Patients receiving \> 6 mg / day of prednisone or equivalent at time of * Patients who have received ATG within 14 days of enrollment * Patients who have received donor lymphocyte infusion (DLI) within 28 days of enrollment. * Patients who have received alemtuzumab within 28 days of enrollment. * Patients with other uncontrolled infections (including HIV/AIDS). Uncontrolled infection is defined as the presence of 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 uncontrolled infection. * Patients with active acute GVHD grades II-IV.