Itacitinib and Tocilizumab for Steroid Refractory Acute Graft Versus Host Disease

Inclusion Criteria: * Adult men and women who are at least 18 years of age * Recipients of their first allogeneic hematopoietic stem cell transplant from any donor source (including bone marrow, mobilized peripheral blood, cord blood) and human leukocyte antigen (HLA)-match (includes matched related, matched unrelated, mismatched unrelated, and haploidentical) * Recipients of allogeneic stem cell transplant after any conditioning regimen intensity and those who have received any GVHD prophylaxis regimen, unless it included tocilizumab and/or itacitinib * Steroid refractory acute GVHD (SR-aGVHD) that has been clinically diagnosed as per the MAGIC criteria and/or pathologically confirmed. Biopsies should be attempted whenever possible according to the investigator's discretion but it is not required as long as alternative diagnoses such as infection or medication side effects have been adequately ruled out. SR-aGVHD is defined as acute GVHD that has failed to exhibit a response after treatment for at least 7 days with a corticosteroid dose of 2 mg/kg of methylprednisolone or prednisone equivalent. SR-aGVHD is also defined as GVHD that flares when steroids are tapered prohibiting further taper. * Adequate renal function determined by creatinine clearance ≥ 40 mL/min measured or calculated by Cockcroft-Gault equation. * Absence of history of irreversible liver disease such as cirrhosis or veno-occlusive disease (VOD) that has not responded to therapy * Total bilirubin and/or transaminases (AST and/or ALT) that are ≤2.5 above institutional upper limit of normal that is not attributable to acute GVHD by biopsy * Non-pregnant females or men and women willing to avoid pregnancy or fathering a child as evidenced by negative pregnancy test (females), non-childbearing potential (history of hysterectomy, oophorectomy, amenorrhea for 12 months) or agree to use barrier or chemical contraception for the duration of the study. * Ability to swallow oral medication * Able to give consent and comply with study visits and procedures Exclusion Criteria: * Primary disease not in complete remission, requiring active treatment, or having required treatment for relapsed disease * Uncontrolled bacterial, viral, or fungal infections which is evidenced by hemodynamic instability, new radiological findings, new signs or symptoms, or persistently positive blood cultures as determined by the investigator. * History of viral infection with HIV * History of infection or exposure to hepatitis B or C with a risk of infection reactivation * History of active or latent tuberculosis infection that has not been adequately treated * Use of any JAK inhibitor or IL-6 antagonists for therapy or prophylaxis of acute GVHD. Continuation of calcineurin inhibitors intended for GVHD prophylaxis is allowed. Resumption of therapeutic dosing of calcineurin inhibitors that is being tapered is also allowed. * Severe organ dysfunction unrelated to GVHD that includes cholestatic disorders or unresolved VOD (defined as ongoing organ dysfunction and bilirubin elevation unrelated to GVHD \> 2.5 the institutional upper limit of normal), clinically significant or uncontrolled cardiac disease (including unstable angina, acute myocardial infarction within 6 months of enrollment, New York Heart Association, Class III or IV congestive heart failure, circulatory collapse requiring vasopressor or inotropic support, or arrhythmia that requires therapy) or clinically significant respiratory disease that requires mechanical ventilation support or 50% or greater supplemental oxygen.. * Receipt of live attenuated vaccine or the need for such a vaccine during the duration of the study * Treatment with any other investigational agent within 7 days of enrollment (or 5 half-lives, whichever is greater) * Treatment with any JAK inhibitor or IL-6 antagonist after stem cell transplant. Treatment with a JAK inhibitor before transplant is allowed. Treatment with IL-6 antagonist before transplant is allowed only if last dose was at least 4 weeks prior to transplant. * Known allergies or sensitivities to itacitinib or tocilizumab * Pregnant, breast-feeding, or unwilling or unable to avoid pregnancy or fathering a child. Pregnant women are excluded from this study as animal studies have shown that tocilizumab crosses the placenta and can interfere with fetal development in animal studies. Furthermore, itacitinib has been associated with embryo-fetal toxicity in animal studies