A two-stage design. An open, non-randomized, 3+3 dose escalating scheme will be used in the first stage of the study. A randomized (1:1) phase II open label study of DSC compared to Investigator choice Best Available Therapy (BAT) in allogeneic hematopoietic stem cell transplant recipients with Grades II-IV steroid refractory acute graft vs. host disease in the second part of the study. Patients in each phase will receive 2 doses of DSC. In the second part (Phase II) additional doses (up to 6 doses) may be given depending on response.||No cross-over are planned in the second stage of the study.