The clinical trial is designed as a single institution, open label, non-randomized Phase I/II trial of MVST in transplant recipients, designed as 3-cohort dose escalation Phase I followed by a 20 subject extension Phase II at the maximum tolerated dose of cells. Safety will be monitored continuously for a period of 6 weeks post T cell transfer. The primary safety endpoint will be the occurrence of dose limiting toxicity, defined as the occurrence of Grade IV GVHD or any other SAE that is deemed to be at least probably or definitely related to the investigational product. The primary efficacy endpoint for the phase II will be the proportion of CMV reactivation requiring treatment at day 100 post transplant. Secondary endpoints are technical feasibility of MSVT manufacture, patterns of virus reactivation by PCR, and clinical disease from EBV, Ad, BK, day 100 non-relapse mortality.