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).