Extracorporeal Photopheresis and Mesenchymal Stem Cell Infusion for GVHD

Inclusion Criteria: -One of the following diagnoses: --High risk aGVHD, either biopsy proven or clinical diagnosed as defined by either: * Skin stage 4 * Lower gastrointestinal (GI) stage ≥ 3 * Liver stage ≥ 3 * Skin stage 3 and lower GI or liver stage ≥ 2 GVHD * Hyper-acute GVHD as defined by aGVHD within the first 14 days of transplant * Overall grade 2-4 aGVHD with high-risk disease identified by the Viracor Eurofins Symptomatic Onset or Post-Treatment Algorithm OR: --Steroid refractory aGVHD (either biopsy proven or clinical diagnosed) as defined by any one of the following criteria per NCCN (National Comprehensive Cancer Network) Guidelines for Hematopoietic Cell Transplantation (HCT): * Progression of aGVHD within 3-5 days of therapy onset with ≥ 2 mg/kg/day of methylprednisolone or equivalent * Failure to improve within 5-7 days of treatment initiation (2 mg/kg/day of methylprednisolone or equivalent) * Incomplete response after more than 28 days of immunosuppressive treatment including steroids (2 mg/kg/day of methylprednisolone or equivalent) * Hct \> 27 and plts \> 50,000 x10\^9/L (may be achieved via transfusion on ECP days) * Candidate for appropriate vascular access for ECP, which may include: (1) peripheral IV with 16 or 17 gauge Fistula needle; (2) central venous access device (apheresis catheter, tunneled central vascular access device), (3) vortex implanted port; (4) Bard POWERFLOW® implanted port * Eastern Cooperative Oncology Group Performance status ≤ 3 * Participants who underwent an allogeneic hematopoietic stem cell transplantation from any donor source * Participants must have the ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Active malignancy * Contraindication to photopheresis, including any of the following: (1) known sensitivity to psoralen compounds such as 8-MOP; (2) comorbidities that may result in photosensitivity; (3) aphakia; (4) insufficient weight/circulating volume (defined by photopheresis machine characteristics); (5) hemodynamic instability; (6) platelet count \< 20 x 109/μL despite platelet support; (7) bleeding diathesis; (8) hematocrit \< 27 despite red blood cell support; (9) inability to lie flat for 4 hours; (10) inadequate venous access * Participants with uncontrolled inter-current illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant or breastfeeding women are excluded from this study because chemotherapy involved with RIC (Reduced-Intensity Conditioning) have the significant potential for teratogenic or abortifacient effects. * Any condition that would, in the investigator's judgment, interfere with full participation in the study, including administration of study drug and attending required study visits; pose a significant risk to the participant; or interfere with interpretation of study data. * Known allergies, hypersensitivity, or intolerance to any of the study medications, excipients, or similar compounds. * Progressive underlying malignant disease or post-transplant lymphoproliferative disease