The aim of this study is to determine the safety and efficacy of very early infusion of MVSTr cells directed against the four most common viruses causing complications after T-depleted SCT. GMP-grade allogeneic MVSTr from the stem cell donor will be generated using or peripheral blood mononuclear cells (PBMCs) pulsed with overlapping peptide libraries of immunodominant antigens from CMV, EBV, Ad, and BKV and expanded in IL-7 and IL-15 followed by IL-2 for 14 days. A fraction of the routine donor leukapheresis for lymphocytes obtained prior to stem cell mobilization will be used to generate the MVST cells. MVST passing release criteria will be cryopreserved ready for infusion post SCT.