In this research study, the investigators want to learn more about the use of donor-derived viral specific T-cells (VSTs) to treat viral infections that occur after allogeneic stem cell transplant. A viral specific T cell is a T lymphocyte (a type of white blood cell) that kills cells that are infected (particularly with viruses). Allogeneic means the stem cells come from another person. These VSTs are cells specially designed to fight the virus infections that can happen after a bone marrow transplant.

The investigators are asking people who have undergone or will undergo an allogeneic stem cell transplant to enroll in this research study, because viral infections are a common problem after allogeneic stem cell transplant and can cause significant complications including death.

Stem cell transplant reduces a person's ability to fight infections. There is an increased risk of getting new viral infections or reactivation of viral infections that the patient has had in the past, such as cytomegalovirus (CMV), Epstein-Barr virus (EBV), adenovirus (ADV), BK virus (BKV), and JC virus. There are anti-viral medicines available to treat these infections, though not all patients will respond to the standard treatments. 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 the investigators are trying to find an easier way to treat these infections.

The stem cell matched donor will be asked to provide a blood donation for the VSTs generation. In the laboratory, the investigators will treat this blood sample to select out the cells that will help fight viruses. The cells will be grown with peptides (protein fragments that represent parts of the virus that will encourage the donor immune cells to grow). The cells will be grown in the laboratory so that there is a stock of virus fighting cells for the patient to use in the future. The investigators will freeze the cells and store them in a freezer in the laboratory.

If the patient has signs of virus in their blood after the transplant, they will be given the cells to help fight the infection. If there are signs that the cells are helping fight the infection, more cells may be given. The patient may get the cells up to 5 times, with 21 days between each treatment (this timeframe may be shortened to 14 days for patients with no evidence of viral response). If the patient does not show signs of a virus, the cells will stay in the freezer.

Following VST infusion, (s)he will be monitored with physical exams daily while inpatient and weekly while outpatient as well as blood tests weekly until 30 days after the last infusion of cells. The patient will have 3 teaspoons (15 mL) of blood drawn and urine collected before each cell infusion and then once a week after each infusion for 4 weeks and then once a month if possible for 1 year after the last infusion, all to monitor for the viral response.

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
• Recipient must have achieved engraftment with ANC ≥ 500

Exclusion Criteria:

• Active acute GVHD grades II-IV
• Uncontrolled bacterial or fungal infection
• Uncontrolled relapse of malignancy requiring treatment with chemotherapy
• Infusion of ATG or alemtuzumab within 2 weeks of VST infusion