A Study to Evaluate Steroid-free Treatment for Standard-Risk aGVHD (BMT CTN 1501)

Inclusion Criteria: 1. Patients with standard-risk acute GVHD, according to refined Minnesota Criteria. Refined Minnesota Criteria are available at https://redcap.ahc.umn.edu/surveys/?s=bNmFhseJIf. Standard-risk acute GVHD according to the refined Minnesota Risk Criteria requires meeting one of the criteria below: 1. Single organ involvement (Stage 1-3 skin, Stage 1 upper GI, or Stage 1-2 lower GI) 2. Multiple organ involvement (Stage 1-3 skin plus stage 1 upper GI, Stage 1-3 skin plus stage 1 lower GI, Stage 1-3 skin plus stage 1 lower GI plus stage 1 upper GI, Stage 1-3 skin plus stage 1-4 liver, or Stage 1 lower GI plus stage 1 upper GI) 2. Acute Minnesota Standard Risk GVHD requiring systemic immune suppressive therapy. 3. Acute GVHD developing after allogeneic hematopoietic cell transplantation using either bone marrow, peripheral blood, or umbilical cord blood. Recipients of non-myeloablative, reduced intensity conditioning and myeloablative transplants are eligible. All allogeneic donor sources are permitted, including siblings, unrelated donors, human leukocyte antigen (HLA)-haploidentical related donors and umbilical cord blood. 4. Patients NOT receiving systemic immune suppressive therapy for treatment of active GVHD (topical skin and GI corticosteroids are allowed). 5. Ability to tolerate oral or enterically-administered medications. 6. Patients of all ages. 7. Absolute neutrophil count (ANC) greater than 500/µL. 8. Biopsy confirmation of GVHD is not required. Enrollment should not be delayed for biopsy or pathology results unless local institutional practice mandates biopsy confirmation to make a GVHD treatment decision. 9. Written informed consent and/or assent from patient, parent or guardian. 10. Collection of a 5 ml blood sample (red top for serum) from the patient for Ann Arbor Scoring and ready to be shipped immediately after randomization. Exclusion Criteria: 1. Patients receiving sirolimus (for any indication including GVHD prophylaxis) within 14 days of screening for enrollment. 2. Relapsed, progressing or persistent malignancy requiring withdrawal of systemic immune suppression. 3. Patients with acute GVHD developing after a donor lymphocyte infusion. 4. Active or recent (within 7 days) episode of transplant associated microangiopathy. 5. Patients with uncontrolled infections will be excluded. Infections are considered controlled if appropriate therapy has been instituted and, at the time of enrollment, no signs of progression are present. Progression of infection is defined as hemodynamic instability attributable to sepsis, new symptoms, worsening physical signs or radiographic findings attributable to infection. Persisting fever without other signs or symptoms will not be interpreted as progressing infection. 6. Patients unlikely to be available for evaluation at the transplant center on Day 28 and 56 of therapy. 7. A clinical presentation resembling de novo chronic GVHD or overlap syndrome developing before or present at the time of enrollment. 8. Patients receiving corticosteroids for any indication within 7 days before the onset of acute GVHD, except the following: Stable replacement doses of corticosteroids for adrenal insufficiency are permitted (e.g. hydrocortisone total dose of 10-12 mg/m\^2/day or prednisone 5-7.5mg daily or equivalent). Corticosteroids administered as premedication before transfusion of blood products or before intravenous medications to prevent infusion reactions are allowed. 9. Patients who are pregnant or breastfeeding. 10. Females of childbearing potential (FCBP) or a man who has sexual contact with a FCBP and is unwilling to use effective birth control for the duration of the study. 11. Patients on dialysis. 12. Patients on mechanical ventilation. 13. Patients with severe hepatic sinusoidal obstruction syndrome who in the judgment of the treating physician are not expected to have normalized bilirubin by Day 56 after enrollment. 14. Patients with a history of hypersensitivity to sirolimus or any component of the formulation.