Multivirus-specific cytotoxic T lymphocytes (AlloVir)

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.