The subjects eligible for this trial have a type of blood cell cancer, other blood disease or a genetic disease for which they will receive a stem cell transplant. The donor of the stem cells will be either the subject's brother or sister, or another relative, or a closely matched unrelated donor. The Investigators are asking subjects to participate in this study which tests if blood cells from the subject's donor that have been grown in a special way, can prevent or be a effective treatment for early infection by five viruses - Epstein Barr virus (EBV), cytomegalovirus (CMV), adenovirus, BK virus (BKV) and human herpes virus 6 (HHV6).

The Investigators have grown T cells from the subject's stem cell donor in the laboratory in a way that will train them to recognize the viruses and control them when the T cells are given after a transplant. This treatment with specially trained T cells (also called cytotoxic T cells or "CTLs") has had activity against three of these viruses (CMV, EBV and Adenovirus) in previous studies. In this study the Investigators want to see if they increase the number of viruses that can be targeted to include BKV and HHV6 using a simple and fast approach to make the cells.

The Investigators want to see if they can use a kind of white blood cell called T lymphocytes (or T cells) to prevent and treat adenovirus, CMV, EBV, BKV and HHV6 in the early stages of reactivation or infection.

To make the CTLs, subject's donors' cells were mixed with small pieces of proteins, called peptides that come from adenovirus, CMV, EBV, BKV and HHV6. These peptides stimulate donor T cells that react against the viruses to grow and train the donor T cells to kill cells that are infected with CMV, EBV, adenovirus, BKV and HHV6. Once sufficient numbers of T cells were made, they were tested to make sure they would target the cells infected with these viruses but not the normal cells. Then the cells were frozen.

When the Investigators think the subject needs them, the subject's donor's CTL cells will be thawed and injected into the intravenous line. To prevent an allergic reaction, prior to receiving the CTLs the subject may be given diphenhydramine (Benadryl) and acetaminophen (Tylenol). After the subject receives the cells, Investigators will monitor the levels of these five viruses in the blood. They will also take blood to see how long the T cells they gave the subject are lasting in the body.

If the CTL infusion has helped the subjects infection or if they have had a treatment, for example with steroid drugs that might have destroyed the T cells the subject was given, then they are allowed to receive up to 2 more doses of the cells.

The first part of this study was a dose escalation study. That means that at the beginning, patients were started on the lowest dose (1 of 3 different levels) of T cells. The next group of patients were started at a higher dose. This process continued until all 3 dose levels were studied. They would now like to enroll more patients at the highest dose level to get more information about how the T cells work.

Subjects will continue to be followed by their transplant doctors after the injection. The subject will either be seen in the clinic or they will be contacted by a research nurse to follow up for this study every week for 6 weeks then at 8 week and 3, 6 and 12 months. The subject may have other visits for their standard care. Subjects will also have regular blood tests done to follow their counts and the viral infection. To learn more about the way the T cells are working in the body, up to an extra 30-40 ml (6-8 teaspoons) of blood will be taken before the infusion and then at 1, 2, 4, 5, 6 and 8 weeks and 3 months. Blood should come from the central intravenous line, and should not require extra needle sticks.

If subjects experience a positive response or are taking medicines (such as steroids) that may affect how long T cells stay in the body, they may be able to receive up to two additional doses of the T cells at the same initial dose level from 28 days after their initial dose. After each T-cell infusion, they will be monitored as described above.

Study Duration: Subjects will be on study for approximately one year. If they receive additional doses of the T cells as described above, they will be followed until 1 year after their last dose of T-cells.

Inclusion Criteria:

Patients will be eligible following any type of allogeneic transplant to receive CTLs as prevention or for early reactivations as defined below.

1. Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells within 12 months.

2. Prevention for patients at risk of CMV, adenovirus, EBV, BK virus, or HHV6 infection

3. Treatment of reactivation or infection which is defined for each virus as below

   • CMV- CMV antigenemia is monitored at least weekly post transplant. Reactivation is defined at CMV antigenemia with <10 leukocytes positive or elevated PCR. If any patient develops CMV antigenemia with >10 leukocytes positive or clinical evidence of CMV infection (defined as the demonstration of CMV by biopsy specimen from visceral sites (by culture or histology) either pre or after CTL infusions, standard treatment with Ganciclovir, and/or Foscarnet and Immunoglobulins will be initiated. Patients may receive CTLs for antigenemia or elevated PCR without visceral infection.
   • Adenovirus- Adenovirus infection will be defined as the presence of adenoviral positivity as detected by PCR or culture from ONE site such as stool or blood or urine or nasopharynx.

   Adenovirus disease will be defined as the presence of adenoviral positivity as detected by culture from more than two sites such as stool or blood or urine or nasopharynx.

   In patients who meet the criteria for disease Cidofovir may be added unless the subject could not tolerate this agent due to nephrotoxicity. Patients may receive CTLs for elevated PCR in blood or stool.

   • EBV- EBV-LPD is defined according to recent guidelines as proven EBV-LPD defined by biopsy or probable EBV-LPD defined as an elevated EBV DNA level associated with clinical symptoms (adenopathy or fever or masses on imaging) but without biopsy confirmation. Patients with EBV DNA reactivation only may receive CTLs on study. Patients with proven or probable EBV-LPD should also receive Rituxan
   • BK virus- Patients post transplant may develop asymptomatic BKV viruria or viremia. BK reactivation will be defined as detection of elevated BK levels by PCR in blood or urine while disease will be defined as detection in multiple sites or in one site with symptoms. Cidofovir has been administered intravenously in a low dose (i.e. up to 1 mg/kg 3 times weekly, without probenecid) or a high dose (ie, 5 mg/kg per week with probenecid) to HSCT patients with BK infections but no randomized trials are available proving its clinical efficacy. In patients who meet the criteria for disease Cidofovir may be added unless the subject could not tolerate this agent due to nephrotoxicity.
   • HHV6- HHV6 reactivation will be defined as detection of elevated HHV6 levels by PCR in blood while disease will be defined as detection in multiple sites or in one site with symptoms. Ganciclovir, Cidofovir, and foscarnet have variable in vitro activity against HHV-6, and may have a role in treating HHV-6-associated disease - hence one or more of these agents will be added in patients with disease.

4. Treatment may be given to eligible patients with a single or multiple infections. Patients with multiple infections with one or more reactivation and one or more controlled infection are eligible to enroll.

5. Clinical status at enrollment to allow tapering of steroids to less than 0.5 mg/kg/day prednisone.

6. Karnofsky/Lansky score of ≥ 50

7. ANC greater than 500/µL.

8. Bilirubin </= 2x upper limit normal

9. AST </= 3 x upper limit normal

10. Serum creatinine </= 2 x upper limit normal

11. HgB > 8.0

12. Pulse oximetry of > 90% on room air

13. Available multivirus-specific CTLs

14. Negative pregnancy test in female patients if applicable (childbearing potential who have received a reduced intensity conditioning regimen).

15. Written informed consent and/or signed assent line from patient, parent or guardian.

Exclusion Criteria:

1. Patients receiving ATG, or Campath or other immunosuppressive T cell monoclonal antibodies within 28 days of screening for enrollment.

2. Patients with other uncontrolled infections. For bacterial infections, patients must be receiving definitive therapy and have no signs of progressing infection for 72 hours prior to enrollment. For fungal infections patients must be receiving definitive systemic anti-fungal therapy and have no signs of progressing infection for 1 week prior to enrollment.

   Progressing infection is defined as 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 progressing infection.

3. Patients who have received donor lymphocyte infusion (DLI) within 28 days.

4. Patients with active acute GVHD grades II-IV.

5. Active and uncontrolled relapse of malignancy