This research trial is designed to study the safety and effectiveness of combining the study drug, Natalizumab (Tysabri®) with the use of steroids to treat acute GVHD in patients at the earliest stages of clinical symptoms, but, by using a proprietary method developed at the University of Michigan and the Icahn School of Medicine at Mount Sinai, are predicted to be at high risk for not responding to steroid therapy, the standard of care.