MSC and HSC Coinfusion in Mismatched Minitransplants

Inclusion Criteria: * Theoretical indication for a standard allo-transplant, but not feasible because: Age \> 55 yrs. Unacceptable end organ performance. Patient's refusal. * Indication for a standard auto-transplant: perform mini-allotransplantation 2-6 months after standard autotransplant. * Male or female; fertile female patients must use a reliable contraception method * Age ≤ 75 year old * Informed consent given by patient or his/her guardian if of minor age. * One or two HLA mismatches with PBSC: * One antigenic mismatch at HLA-A or -B or -C or -DRB1 or -DQB1 * Two allelic mismatches at HLA-A or -B or -C or -DRB1 or -DQB1 * One antigenic mismatch: 1 allelic mismatch at HLA-A or -B or -C or -DRB1 or -DQB1. * One antigenic mismatch at -DQB1 and one other antigenic mismatch at HLA-A or -B or -C or -DRB1 * Patients with one single allelic mismatch at HLA-A or -B or -C or -DRB1 or -DQB1 can also be included in the protocol. * Hematological malignancies confirmed histologically and not rapidly progressing: * AML in complete remission * ALL in complete remission * CML unresponsive/intolerant to Imatinib but not in blast crisis * Other myeloproliferative disorders not in blast crisis and not with extensive myelofibrosis * MDS with \<5% blasts * Multiple myeloma not rapidly progressing * CLL * Non-Hodgkin's lymphoma (aggressive NHL should be chemosensitive) * Hodgkin's disease Exclusion Criteria: * Any condition not fulfilling inclusion criteria * HIV positive * Terminal organ failure, except for renal failure (dialysis acceptable) * Cardiac: Symptomatic coronary artery disease or other cardiac failure requiring therapy; ejection fraction \<35%; uncontrolled arrhythmia; uncontrolled hypertension * Pulmonary: DLCO \< 35% and/or receiving supplementary continuous oxygen * Hepatic: Fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis, esophageal varices, a history of bleeding esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction evinced by prolongation of the prothrombin time, ascites related to portal hypertension, bacterial or fungal liver abscess, biliary obstruction, chronic viral hepatitis with total serum bilirubin \> 3 mg/dL, and symptomatic biliary disease * Uncontrolled infection, arrhythmia or hypertension * Previous radiation therapy precluding the use of 2 Gy TBI * 10/10 HLA-A, -B, -C, DRB1 and DQBI allele-matched donor fit to/willing to donate PBSC.