This clinical trial will study ruxolitinib-based treatment of acute graft-versus-host-disease (GVHD) that developed following allogeneic hematopoietic cell transplant. Acute GVHD occurs when donor cells attack the healthy tissue of the body. The most common symptoms are skin rash, jaundice, nausea, vomiting, and/or diarrhea. The standard treatment for GVHD is high dose steroids such as prednisone or methylprednisolone, which suppresses the donor cells, but sometimes there can be either no response or the response does not last. In these cases, the GVHD can become dangerous or even life threatening. High dose steroid treatment can also cause serious complications. Researchers have developed a system, called the Minnesota risk system, to help predict how well the GVHD will respond to steroids based on the symptoms present at the time of diagnosis. The Minnesota risk system classifies patients with newly diagnosed acute GVHD into two groups with highly different responses to standard steroid treatment and long-term outcomes. This protocol maximizes efficiency because all patients with grade II-IV GVHD are eligible for screening and treatment is assigned according to patient risk. Patients with lower risk GVHD, Minnesota standard risk, have high response rates to steroid treatment. In this trial the researchers will test whether ruxolitinib alone is as effective (non-inferior) as steroid-free therapy and safe. Patients will be randomized to two different doses of ruxolitinib to identify the dose which maximizes efficacy while minimizing toxicities such as hematologic and infectious toxicities. Patients with higher risk GVHD, Minnesota high risk, have unacceptable outcomes with systemic corticosteroid treatment alone and the researchers will test whether adding ruxolitinib, a proven effective second line GVHD treatment, can improve outcomes when added to systemic corticosteroids as first line treatment.