Eligible subjects on NHLBI protocol 13-H-0144 will receive a single early infusion of MVST within 30 days (target day +14, range 0-30 days) post SCT. Phase I safety monitoring will continue for 6 weeks. Viral reactivation (CMV, EBV, Ad, BK) will be monitored by PCR by serial blood sampling. The only antiviral prophylaxis given will be acyclovir to prevent herpes simplex and varicella zoster reactivation. Subjects with rising PCR exceeding threshold for treatment, or those with clinically overt viral disease will receive conventional antiviral treatment. Patients developing acute GVHD will receive standard treatment with systemic steroids. These patients are eligible for reinfusion of MVST when steroids are tapered.