A Randomized Phase II Study to Compare the Potential Long-Lasting Positive Effect of Decidual Stromal Cells to the Best Available Treatment in Graft Versus Host Disease

Inclusion Criteria: 1. Signed written study informed consent form once SR-aGvHD is confirmed. 2. Male or female patients aged 18 or older at the time of informed consent. 3. Have undergone HSCT from any donor source (unrelated, sibling, haploidentical) using bone marrow, peripheral blood stem cells, or cord blood. Recipients of non- myeloablative, myeloablative, and reduced intensity conditioning are eligible. 4. Clinically diagnosed Grades II to IV acute GvHD as per standard criteria (Appendix 1) occurring after HSCT requiring systemic immune suppressive therapy. Biopsy of involved organs with aGvHD is encouraged and may be performed as per institutional practices at investigator's discretion for aGvHD management. If performed, the investigator will indicate the results once available and the results are not required prior to study treatment. 5. Confirmed diagnosis of steroid-refractory aGvHD defined as patients administered high dose systemic corticosteroids (methylprednisolone ≥1mg/kg/day (±20%) \[or equivalent prednisone dose ≥1.25 mg/kg/day\]), given alone or combined with calcineurin inhibitors (CNI) and either: A. Progression based on organ assessment after at least 3 days compared to organ stage at the time of initiation of high-dose systemic corticosteroid +/- CNI for the treatment of Grade II-IV aGvHD, OR B. Failure to achieve at a minimum partial response based on organ assessment after 5-7 days compared to organ stage at the time of initiation of high-dose systemic corticosteroid +/- CNI for the treatment of Grade II-IV aGvHD, OR C. Patients who fail corticosteroid taper defined as fulfilling either one of the following criteria: 1. Requirement for an increase in the corticosteroid dose to methylprednisolone ≥1 mg/kg/day (or equivalent prednisone dose ≥1.25 mg/kg/day) OR 2. Failure to taper the methylprednisolone dose to \<0.5 mg/kg/day (or equivalent prednisone dose \<0.6 mg/kg/day) for a minimum 7 days. Exclusion Criteria: 1. Has received systemic treatment for aGvHD apart from steroids. Standard aGvHD prophylaxis and treatment medications initiated before randomization including systemic corticosteroids, calcineurin inhibitors (CNI) (cyclosporine or tacrolimus), mycophenolate mofetil, and topical corticosteroid therapy may be continued, per institutional guidelines. 2. Clinical presentation resembling de novo chronic GvHD or GvHD overlap syndrome with both acute and chronic GvHD features (as defined by Jagasia, et al. 2015) 3. Presence of an active uncontrolled infection including significant bacterial, fungal, viral or parasitic infection requiring treatment. Infections are considered controlled if appropriate therapy has been instituted and, at the time of screening, 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. Expections may be allowed upon approval by the Sponsor. 4. Known human immunodeficiency virus infection (HIV). 5. Significant respiratory disease including patients who are on mechanical ventilation or who have resting O2 saturation \<90% by pulse-oximetry. 6. Presence of severely impaired renal function defined by serum creatinine \> 2 mg/dL (\>176.8 μmol/L), renal dialysis requirement, or have estimatedcreatinine clearance \<30 ml/min measured or calculated by Cockroft Gault equation (confirmed within 48h prior to study treatment start). 7. Any corticosteroid therapy for indications other than aGvHD at doses \> 1 mg/kg/day methylprednisolone (or equivalent prednisone dose 1.25 mg/kg/day) within 7 days of Screening. Routine corticosteroids administered during conditioning or cell infusion is allowed. 8. History of progressive multifocal leuko-encephalopathy (PML). 9. Previous participation in a study of any investigational treatment agent within 30 days or within 5 half-lives of the study treatment, whichever is greater. 10. Any condition that would, in the Investigator's judgment, interfere with full participation in the study, including administration of study treatment and attending required study visits; pose a significant risk to the patient; or interfere with interpretation of study data. 11. Known allergies, hypersensitivity, or intolerance to systemic immunosuppressive therapy. 12. Pregnant or nursing (lactating) women