The purpose of this research study is to learn more about the use of viral specific T-lymphocytes (VSTs) to prevent viral infections that may happen after allogeneic stem cell transplant. Allogeneic means the stem cells come from another person. VSTs are cells specially designed to fight viral infections that may happen after a stem cell transplant (SCT).

Stem cell transplant reduces your ability to fight infections. Viral infections are a common problem after transplant and can cause significant complications. Moreover, treatment of viral infections is expensive and time consuming, with families often administering prolonged treatments with intravenous anti-viral medications, or patients requiring prolonged admissions to the hospital. The medicines can also have side effects like damage to the kidneys or reduction in the blood counts, so in this study we are trying to find a way to prevent these infections.

Inclusion Criteria:

• Recipient must be at least 21 days after stem cell infusion
• Clinical status must allow tapering of steroids to < 0.5mg/kg prednisone or other steroid equivalent

Exclusion Criteria:

• Patients who have developed viral infection or reactivation will be ineligible for prophylactic infusions of VSTs
• Active acute GVHD grades II-IV
• Uncontrolled relapse of malignancy
• Infusion of ATG or alemtuzumab within 2 weeks of VST infusion. Additionally, in patients who received alemtuzumab as part of their conditioning regimen, alemtuzumab levels will be collected in the second week following stem cell infusion. The level must be less than, or equal to, 0.15 prior to infusion of VSTs. In patients with level greater than 0.15, alemtuzumab levels can be checked serially until a level ≤ 0.15 is obtained. They would become eligible for prophylactic VST infusion at that point if there is still no evidence of viral infection at that time.