Allogeneic Transplantation From Related Haploidentical Donors

Inclusion Criteria: * Age ≥ 50 years with hematologic malignancies treatable by a mixed chimera allogeneic HCT. * For patients ≤ 50 years of age with hematologic malignacies treatable with mixed chimera HCT who because of pre-exisiting medical conditions or prior therapy are considered to be at high risk for regimen-related toxicity associated with conventional transplants. * Indolent advanced stage NHL, CLL, HD - Must have received and failed front-line therapy. * Multiple myeloma (Stage II or III) - Must have received prior chemotherapy. Consolidation after prior autografting is permitted. * AML/ALL - Must be in complete hematologic remission and have received cytotoxic chemotherapy at some stage before transplant. Patients with molecular or cytogenetic relapse will be accepted providing a donor is available. Patients with persistent or refractory disease will be considered on a case by case basis and transplants must be approved by the principal investigator. * CML - Patients will be accepted in chronic or accelerated phase. Patients who have received prior autografts after high dose therapy or have undergone intensive chemotherapy for either peripheral blood stem cell mobilization or treatment of advanced CML may be enrolled provided they are in CR, chronic phase or accelerated phase. * MDS - All patients with MDS will be eligible for this protocol, however, those patients with \>10% blasts will require chemotherapy to reduce the blast % to \< 10%. * SAA - Patients with severe aplastic anemia who have failed front line therapy. * A fully HLA-identical sibling donor is not available. * A matched unrelated donor has not been identified. * A haploidentical related donor is available who is in good health and does not have contraindications to donation. Exclusion Criteria: * Patients with rapidly progressive intermediate or high grade NHL * Uncontrolled CNS involvement with disease * Fertile men * Women unwilling to use contraceptive techniques during and for 12 months following treatment * Females who are pregnant * Cardiac function: ejection fraction \< 30% or cardiac failure requiring therapy * Pulmonary: DLCO \< 40% predicted and/or receiving supplementary continuous oxygen * Liver function abnormalities: elevation of bilirubin to \> 4 mg/dl and/or transaminases \> 3x the upper limit of normal. If hyperbilirubinemai is due to a known cause that will not increase the risks of transplant, than this upper limit may be exceeded. * Renal: creatinine clearance \< 50 cc/min (24 hour urine collection) * Karnofsky performance score \< 60% * Patients with poorly controlled hypertension. * Documented fungal disease that persists despite treatment * HIV positive patients. * Hepatitis B and C positive patients will be evaluated on a case by case basis * Psychiatric disorders or psychosocial problems which in the opinion of the primary physician or principal investigator would place the patient at unacceptable risk from this regimen.