Reduced Intensity Conditioning and Haploidentical Related Bone Marrow for Patients With Hematologic Diseases

Inclusion Criteria: * Must be \<75 years old with no 7/8 or 8/8 HLA-matched sibling donor * One or more potential related mismatched donors (e.g. biologic parent (s) or siblings (full or half) or children). Low resolution using DNA based typing at HLA-A, -B and -DRB1 for potential haploidentical donors is required. * All diseases listed below are advanced hematologic malignancies not curable by conventional chemotherapy. Responses to conventional treatment range from zero to 30% but are typically short lived. * Acute Lymphoblastic Leukemia (ALL) in first complete remission (CR1) that is NOT considered favorable-risk. * Acute Myelogenous Leukemia (AML) in first complete remission (CR1) that is NOT considered as favorable-risk. * Acute Leukemias in 2nd or subsequent CR * Biphenotypic/Undifferentiated/Prolymphocytic Leukemias in first or subsequent CR, adult T-cell leukemia/lymphoma in first or subsequent CR * Burkitt's lymphoma in CR2 or subsequent CR * Natural killer cell malignancies after response to initial therapy * Chronic myelogenous leukemia: all types except refractory blast crisis. * Large-cell lymphoma, Hodgkin lymphoma and multiple myeloma with chemotherapy sensitive disease that has failed or patients who are ineligible for an autologous transplant. * Chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), marginal zone B-cell lymphoma, follicular lymphoma, which have progressed within 12 months of achieving a partial or complete remission. * Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy if chemotherapy sensitive. * Refractory leukemia or MDS These patients may be taken to transplant in aplasia after induction or re-induction chemotherapy or radiolabeled antibody. * Bone marrow failure syndromes, except for Fanconi Anemia * Myeloproliferative syndromes * Adequate organ function is defined as: * Cardiac: Absence of decompensated congestive heart failure, or uncontrolled arrhythmia and left ventricular ejection fraction \> 35%. For children that are not able to cooperate with multigated acquisition scan (MUGA) and echocardiography, such should be clearly stated in the physician's note * Pulmonary: Diffusing capacity of lung for carbon monoxide (DLCO) \> 30% predicted, and absence of O2 requirements. For children that are not able to cooperate with pulmonary function tests (PFTs), a pulse oximetry with exercise should be attempted. If nether test can be obtained it should be clearly stated in the physician's note. * Liver: Transaminases \< 5 x upper limit of normal and bilirubin \< 3 x upper limit of normal * Renal: serum creatinine \< 2.0 mg/dl (adults) or glomerular filtration rate (GFR) \>40 mL/min/1.73m2 (peds). Patients with a creatinine \> 1.2 mg/dl or a history of renal dysfunction must have glomerular filtration rate (GFR) \> 40 mL/min/1.73m2. * Adequate performance status is defined as Karnofsky score ≥ 60% (\> 16 years of age) or Lansky score ≥ 50 (pediatrics) * If recent mold infection e.g. Aspergillus - must have minimum of 30 days of appropriate treatment before bone marrow transplant (BMT) and infection controlled and be cleared by Infectious Disease. * Second BMT: Must be \> 3 months after prior myeloablative transplant. * Patients must be ineligible for autologous transplantation due to prior autologous transplant, an inadequate autologous stem cell harvest, inability to withstand a myeloablative preparative regimen, or clinically aggressive/high risk disease. * Patients are eligible for transplantation if there is no evidence of progressive disease by imaging modalities or biopsy. Persistent PET activity, though possibly related to lymphoma, is not an exclusion criterion in the absence of CT changes indicating progression. * Patients with stable disease are eligible for transplantation if the largest residual nodal mass is \< 5 cm (approximately). For patients who have responded to preceding therapy, the largest residual mass must represent a 50% reduction and be \< 7.5 cm (approximately). * Voluntary written consent (adult or parental/guardian) Exclusion Criteria: * Available and clinically suitable 5-6/6 HLA-A, B, DRB1 matched sibling donor * Pregnant or breastfeeding * Evidence of HIV infection or known HIV positive serology * Current active serious infection * Unless in post-chemotherapy and radioimmunoconjugated antibody induced aplasia, when he/she would be eligible, patients with acute leukemia in morphologic relapse/ persistent disease defined as \> 5% blasts in normocellular bone marrow OR any % blasts if blasts have unique morphologic markers (e.g. Auer rods) or associated cytogenetic markers that allows morphologic relapse to be distinguished are not eligible. * Chronic myeloid leukemia (CML) in refractory blast crisis * Large cell lymphoma, mantle cell lymphoma and Hodgkin disease that is progressive on salvage therapy. Stable disease is acceptable to move forward provided it is non-bulky. * active central nervous system malignancy