Mesenchymal Stem Cells (MSCs) for Steroid Refractory Acute GVHD (SR-aGVHD)

Inclusion Criteria: 1. Minimum 18 years of age who have undergone hematopoietic cell transplantation (HCT), from any donor source donor (including HLA-matched related and unrelated, haploidentical and umbilical cord donors) with any conditioning regimen 2. Clinically diagnosed Grades II to IV acute GVHD as per standard criteria occurring within 100 days of HCT 3. Confirmed diagnosis of steroid refractory aGVHD defined as patients administered high-dose systemic corticosteroids (methylprednisolone 2 mg/kg/day \[or equivalent prednisone dose 2.5 mg/kg/day\]), given alone or combined with calcineurin inhibitors (CNI) and either: 1. Progressing based on organ assessment after at least 3 days at the time of initiation of high-dose systemic corticosteroid +/- CNI for the treatment of Grade II-IV aGVHD, OR 2. Failure to achieve at a minimum partial response based on organ assessment after 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 3. Patients who fail corticosteroid taper defined as fulfilling either one of the following criteria: i. Requirement for an increase in the corticosteroid dose to methylprednisolone ≥2 mg/kg/day (or equivalent prednisone dose ≥2.5 mg/kg/day), OR ii. 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. 4. Minimum Karnofsky Performance Level of at least 30 or higher at the time of study entry. Exclusion Criteria: 1. Has received more than one systemic treatment for steroid refractory aGVHD in addition to steroids. 2. Received stem cell therapy in the past 3. Presence of an active uncontrolled infection including significant bacterial, fungal, viral, or parasitic infection requiring treatment 4. Presence of relapsed primary malignancy, or who have been treated for relapse after the HCT was performed, or who may require rapid immune suppression withdrawal as pre-emergent treatment of early malignancy relapse. 5. Evidence of pulmonary infiltrate or hemorrhage based on imaging or requiring high flow oxygen via face mask 6. Patients who have had treatment with any other investigational agent, device, or procedure within 30days (or 5 half-lives, whichever is greater) prior to enrollment. 7. Patients who have received more than one HCT 8. Any medical or psychological condition or situation deemed by the Investigators to put the patient at increased risk of complications or non-compliance. 9. Unresolved veno-occlusive disease 10. HLA antibody screen positive for HLA antibodies specific against the MSCs products 11. ALT or AST \> 5X of upper limit of normal 12. Serum Bilirubin \>2 X of upper limit of normal 13. GFR \<50 ml/min 14. SpO2 \<94% despite being on continuous supplemental oxygen 15. Patients requiring continuous \>4L/minute of supplemental oxygen (irrespective of oxygen saturation)