Age 15-60 yrs Patients for whom allogeneic stem cell transplantation is the preferred treatment option, with the following hematological malignancies:acute myeloid leukemia, acute lymphoblastic leukemia, high risk myelodysplastic syndrome, advanced lymphoproliferative disorders, chronic myeloid leukemia (refractory or intolerant to second-line tyrosine kinase inhibitors), multiple myeloma Informed consent given Patient exclusion criteria Previous allogeneic transplant Progressive malignant disease Significant organ damage as a contraindication to allotransplantation Significant psychiatric or neurological disorder Uncontrolled viral, fungal or bacterial infection Pregnancy HIV positive Patients will receive either myeloablative or reduced intensity conditioning. One or 2 cord blood transplants will be transplanted, followed by infusion of a third-party mesenchymal stem cell transplant Adverse event reporting BHS transplant committee will establish a protocol review committee which will organize a central monitoring of the study. Within the context of allogeneic HSCTx many severe events are likely to occur.