Additional Study Information: Graft versus host disease (GVHD) is a common complication after allogeneic stem cell transplant. It happens when the immune system of the donor is attacking the organs, and usually causes a skin rash, diarrhea, nausea and vomiting, and liver abnormalities. While it is often treated with steroids, some patients are considered steroid-refractory, which means the steroids are not working. This study is testing the combination of two medications, itacitinib and tocilizumab, that have shown some promise in steroid-refractory GVHD. The main purpose of this study is to find out whether the two study drugs are safe in combination because this combination has never been tested before. We will also look at whether the combination works well and has promise to be studied further. We chose this combination because each drug has shown promise in treating patients with steroid-refractory GVHD. After we check the safety of the combination, then the second part of the study will check the efficacy of the combination.