FMT In High-Risk Acute GVHD After ALLO HCT

Inclusion Criteria: * Men or women ≥ 18 years old * Patient has undergone allogeneic hematopoietic cell transplantation from any donor (related or unrelated with any degree of HLA matching) and any donor source (bone marrow, peripheral blood stem cells, or cord blood) for a hematologic malignancy or disorder. Recipients of myeloablative and reduced-intensity conditioning regimens are eligible. * Evidence of myeloid engraftment (eg, absolute neutrophil count ≥ 0.5 × 109/L for 3 consecutive assessments if ablative therapy was previously used). Use of growth factor supplementation is allowed. * Patient must have clinically suspected Grade II to IV aGVHD as per MAGIC criteria. Clinical suspicion of aGVHD by the treating physician is sufficient and biopsies are not required to pathologically confirm aGVHD. However, in situations where alternative diagnoses of drug effects or infection are not adequately ruled out on clinical suspicion alone, biopsies are recommended. - Patients must have a diagnosis of high-risk acute GVHD, defined as either: \-- Steroid-refractory GVHD: * Progressive GVHD after at least 3 days of systemic corticosteroids (≥ 1 mg/kg/day of prednisone equivalent), OR * No improvement in GVHD after at least 7 days on ≥ 1 mg/kg/day of prednisone equivalent or insufficient improvement which warrants the addition of another agent, OR * Flare of GVHD symptoms during taper. * High-risk, treatment-naïve GVHD * AA3 risk by Ann Arbor GVHD scoring risk system * Treatment-naïve: less than 3 days of therapy with systemic corticosteroids (≥ 1 mg/kg/day of prednisone equivalent) * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study and for 3 months after FMT. * Ability to understand and the willingness to sign a written informed consent document, including the willingness to accept risk of unrelated donor stool. * Ability to swallow large capsules. Exclusion Criteria: * Participants who have initiated a new systemic treatment for steroid-refractory GVHD (institutional standard or investigational agent) within the 2 weeks prior to first dose of FMT. Treatment with FMT is allowed once the time since initiation of newest systemic therapy is 2 weeks or longer. * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Delayed gastric emptying syndrome or large hiatal hernia * Known chronic aspiration * Participants with a history of significant allergy to foods not excluded from the donor diet (excluded foods are tree nuts, peanuts, shellfish, eggs) * Pregnant and breast-feeding women are ineligible because they are not eligible for hematopoietic stem cell transplantation. * HIV-positive participants are ineligible. * Participants who are unable to swallow pills. * Participants with end-stage liver disease (cirrhosis) * Participants with acute, active gastrointestinal infection (e.g., typhlitis, diverticulitis, appendicitis) * Participants with inflammatory bowel disease (e.g., ulcerative colitis, Crohn's) * Prior total colectomy