HLA-Compatible Related or Unrelated Donors With CD34+ Enriched, T-cell Depleted Peripheral Blood Stem Cells Isolated by the CliniMACS System in the Treatment of Patients With Hematologic Malignancies

Inclusion Criteria: * Malignant conditions or other life threatening disorders correctable by transplant for which CD34+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as: * AML in 1st remission - for patients whose AML does not have 'good risk' cytogenetic features (i.e. t 8;21, t15;17, inv 16). * Secondary AML in 1st remission * AML in 1st relapse or \> than or = to 2nd remission * ALL/CLL in 1st remission clinical or molecular features indicating a high risk for relapse; or ALL/CLL \> than or = to 2nd remission * CML failing to respond to or not tolerating Imatinib or dasatinib in first chronic phase of disease; CML in accelerated phase second chronic phase or in CR after accelerated phase or blast crisis. * Non-Hodgkins lymphoma with chemoresponsive disease in any of the following categories: 1. intermediate or high grade lymphomas who have failed to achieve a first CR or have relapsed following a 1st remission who are not candidates for autologous transplants. 2. any NHL in remission which is considered not curable with chemotherapy alone and not eligible/appropriate for autologous transplant. * Myelodysplastic syndrome (MDS): RA//RARS/RCMD with high risk cytogenetic features or transfusion dependence as well as RAEB-1 and RAEB-2 and Acute myelogenous leukemia (AML) evolved from MDS, who are not eligible for transplantation and/or unable to enroll onto protocol IRB 08-008. * Chronic myelomonocytic leukemia: CMML-1 and CMML-2. * Multiple Myeloma with disease in the following categories: 1. Patients with relapsed multiple myeloma following autologous stem cell transplantation who have achieved at least partial response following additional chemotherapy. 2. Patients with high risk cytogenetics at diagnosis must have achieved a partial response following autologous stem cell transplantation. Patients must have complex karyotype, del17p, t4;14 and/or t14;16 by FISH and/or del13 by karyotyping. * Other rare lethal disorders of Hematopoiesis and Lymphopoiesis for which a T-cell depleted transplant is indicated (e.g. hemophagocytic lymphohistiocytosis; refractory aplastic anemia or congenital cytopenias; non-SCID lethal genetic immunodeficiencies such as Wiskott Aldrich Syndrome, CD40 ligand deficiency, or ALPS, as well as refractory autoimmune cytopenias, PNH, metabolic storage diseases or heavily transfused congenital hemoglobinopathies). * Accrual to each treatment arm will include up to 30 standard risk and 30 poor risk patients (60 patients/treatment arm) except for Regimen D, which will include 30 patients/treatment arm, all of which will be poor risk by virtue of risks of relapse and/or transplant related mortality. * Standard risk patients will include eligible patients, as defined above, who are receiving transplants as treatment for MDS in RA//RARS/RCMD, AML in 1st or 2nd remission, ALL in 1st CR, NHL in 1st remission, MM in 1st remission, Very Good Partial Response, or 1st Partial Response or CML in the first chronic phase or 1st remission. * All other patients, including those with treatment related malignancies and/or those who have AML derived from MDS, will have received extensive prior chemo/radiotherapy and, therefore, will be considered to be at poor risk of conditioning and transplant related morbidities, and potentially transplant related mortality. Patients with life threatening non-malignant genetic and acquired disorders will also, by virtue of their history of, optional transfusions and/or infection be considered poor risk. Stopping rules for non-relapse related mortality in these heavily treated patients are, therefore, slightly less stringent than patients in the poor risk transplant groups. Stopping rules for the principal endpoints of graft failure and GvHD are the same for all groups. The following inclusion criteria are also required: * Patient's age includes from birth on to \< 70 years old. * Patients may be of either gender or any ethnic background. * Patients must have a Karnofsky (adult) or Lansky (pediatric) Performance Status \> or = to 70% * Patients must have adequate organ function measured by: Cardiac: asymptomatic or if symptomatic then LVEF at rest must be \> or = to 50% and must improve with exercise. Hepatic: \< 3x ULN AST and ≤ to 1.5 total serum bilirubin, unless there is congenital benign hyperbilirubinemia or if the hyperbilirubinemia is directly caused by the disease in which the patient is receiving a transplant (e.g. AML Chloroma obstructing the biliary tree). Patients with higher bilirubin levels due to causes other than active liver disease are also eligible with PI approval e.g. patients with PNH, Gilbert's disease or other hemolytic disorders. Renal: serum creatinine \< than or = to 1.2 mg/dl or if serum creatinine is outside the normal range, then CrCl \> 40 ml/min (measured or calculated/estimated) Pulmonary: asymptomatic or if symptomatic, DLCO \> or = to 50% of predicted (corrected for hemoglobin) * Each patient must be willing to participate as a research subject and must sign an informed consent form. Exclusion Criteria: * Female patients who are pregnant or breast-feeding * Active viral, bacterial or fungal infection * Patient seropositive for HIV-I/II; HTLV -I/II * Presence of leukemia in the CNS. Donor Inclusion Criteria: * Each donor must meet criteria outlined by institutional guidelines * Donor should agree to undergo general anesthesia and bone marrow harvest collection if PBSC yield is inadequate or otherwise not transplantable for whatever reason. Donor Exclusion Criteria * If donors do not meet institutional guidelines, exclusion will be considered.