Inclusion Criteria:

1. Hematological malignancies confirmed histologically and not rapidly progressing:

- Acute myeloid leukemia (AML) in complete remission (CR) (defined as ≤ 5% marrow
blasts and absence of blasts in the peripheral blood);

- Myelodysplastic syndromes (MDS) with ≤ 5% marrow blasts and absence of blasts in
the peripheral blood;

- Chronic myeloid leukemia (CML) in chronic phase (CP);

- Myeloproliferative neoplasms not in blast crisis and not with extensive marrow
fibrosis;

- Acute lymphoid leukemia (ALL)in CR;

- Multiple myeloma not rapidly progressing;

- chronic lymphocytic leukemia (CLL);

- Non-Hodgkin's lymphoma (aggressive NHL should have chemosensitive disease);

- Hodgkin's disease with chemosensitive disease;

2. 10/10 HLA-A, -B, -C, DRB1 and DQBI allele-matched donor fit to/willing to donate
PBSC.

3. Clinical situations:

1. Theoretical indication for a standard allotransplant, but not feasible because:

- Age > 50 yrs;

- Unacceptable end organ performance;

- At the physician's decision;

- Patient's refusal.

2. Indication for a standard auto-transplant: perform mini-allotransplantation 2-6
months after standard autotransplant.

4. Other inclusion criteria:

- Male or female; fertile patients must use a reliable contraception method;

- Age ≤ 75 yrs (children of any age are allowed in the protocol);

- Informed consent given by patient or his/her guardian if of minor age.

Exclusion Criteria:

- Any condition not fulfilling inclusion criteria;

- HIV positive;

- Non-hematological malignancy(ies) (except non-melanoma skin cancer) < 3 years before
nonmyeloablative hematopoietic cell transplantation (HCT);

- Life expectancy severely limited by disease other than malignancy;

- Administration of cytotoxic agent(s) for "cytoreduction" within three weeks prior to
initiating the nonmyeloablative transplant conditioning (Exceptions are hydroxyurea
and imatinib mesylate);

- CNS involvement with disease refractory to intrathecal chemotherapy;

- Terminal organ failure, except for renal failure (dialysis acceptable)

1. Cardiac: Symptomatic coronary artery disease or other cardiac failure requiring
therapy; ejection fraction <35%; uncontrolled arrhythmia, uncontrolled
hypertension;

2. Pulmonary: DLCO < 35% and/or receiving supplementary continuous oxygen;

3. 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;

- Karnofsky Performance Score <70%;

- Patient is a fertile man or woman who is unwilling to use contraceptive techniques
during and for 12 months following treatment;

- Patient is a female who is pregnant or breastfeeding;

- Any condition precluding the use of sirolimus or MMF;

- One HLA mismatch with peripheral blood stem cells (PBSC) fit to/willing to donate.