A Randomized Controlled Pilot Study of Two Doses of Cord Blood Tissue-Derived Mesenchymal Stromal Cells Combined With Ruxolitinib Versus Ruxolitinib Alone for Therapy of Steroid-Refractory Acute Graft Versus Host Disease

Inclusion Criteria: 1. Participants between the ages of 12 years and 80 years (inclusive). 2. Steroid refractory grades II-IV acute GVHD of the Lower GI tract or Liver (including those developing these manifestations after previous acute GVHD of skin) secondary to allogeneic HCT or donor lymphocyte infusion. (Grading, see Appendix I) GVHD with: No improvement after treatment with methylprednisolone at ≥ 2.0 mg/kg/day or equivalent for minimum 7 days, or progressive symptoms after minimum 3 days, or a flare in acute GVHD while on systemic steroids. Participants must have had a biopsy that suggests GVHD; a repeat biopsy to enroll on the study is not necessary. 3. Karnofsky/Lansky Performance score of at least 30 at the time of study entry. 4. Participants who are women of childbearing potential, must be non-pregnant, not breast-feeding, and use adequate contraception. Male patients must use adequate contraception 5. Participants (or legal representative where appropriate) must be capable of providing written informed consent, and assent if indicated. Exclusion Criteria: 1. De novo chronic GVHD 2. Isolated acute GVHD of skin 3. Secondary systemic therapy for acute GVHD ruxolitinib greater than 96 hours before initiation of therapy. 4. Primary treatment with agents other than alpha-1 antitrypsin (AAT) glucocorticoids and ruxolitinib. 5. Participants 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. Adult and pediatric patients with cognitive impairments and/or any serious unstable pre-existing medical condition or psychiatric disorder that can interfere with safety or with obtaining informed consent or compliance with study procedures. 7. Participants with significant supplemental oxygen requirement defined as \>6 L oxygen by nasal cannula. 8. Participants with known allergy to bovine or porcine products.