Haploidentical Donor Bone Marrow Transplant in Treating Patients With High-Risk Hematologic Cancer

Inclusion Criteria: * Chronic myeloid leukemia (CML) in accelerated phase (AP) * Acute myeloid leukemia (AML) with high-risk cytogenetics \[del(5q)/-5, del(7q)/-7, abnormal 3q, 9q, 11q, 20q, 21q, 17p, t(6:9), t(9;22), complex karyotypes (\>= 3 abnormalities)\] in complete remission (CR)1 * AML \>= CR2; patients should have \< 5% marrow blasts at the time of transplant * High-risk ALL defined as: CR1 with high-risk cytogenetics; t(9;22), t(4;11), or hypodiploid (\< 45 chromosomes) for pediatric patients; t(9;22), t(8;14), t(4;11), t(1;19) for adult patients; \> 4 wk to achieve CR1; \>= CR2 (patients should have \< 5% marrow blasts at the time of transplant) * Myelodysplastic syndromes (MDS) (\>int-1 per IPSS) after \>= 1 prior cycle of induction chemotherapy; should have \< 5% marrow blasts at the time of transplant * Multiple myeloma (MM) Stage II or III patients who have progressed after an initial response to chemotherapy or autologous hematopoietic stem cell transplantation (HSCT) or MM patients with refractory disease who may benefit from tandem autologous-nonmyeloablative allogeneic transplant * Chronic lymphocytic leukemia (CLL), non-Hodgkin's lymphoma (NHL) or Hodgkin's Disease (HD) who are ineligible for autologous HSCT or who have resistant/refractory disease and who may benefit from tandem autologous nonmyeloablative allogeneic transplant * Patients who have received a prior allogeneic HSCT and who have either rejected their grafts or who have become tolerant of their grafts with no active graft-versus-host disease (GvHD) requiring immunosuppressive therapy * DONOR: Related donors who are identical for one HLA haplotype and mismatched at the HLA-A, -B, -C or DRB1 loci of the unshared haplotype with the exception of single HLA-A, -B or -C allele mismatches Exclusion Criteria: * Cross-match positive with donor * Patients with suitably matched related or unrelated donors * Patients with conventional transplant options (a conventional transplant should be the priority for eligible patients =\< 50 yr of age who have a related donor mismatched for a single HLA-A, -B or DRB1 antigen) * Central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy * Presence of active, serious infection (e.g., mucormycosis, uncontrolled aspergillosis, tuberculosis) * Karnofsky Performance Status \< 60 for adult patients * Lansky-Play Performance Score \< 60 for pediatric patients * Left ventricular ejection fraction \< 35% * Diffusing capacity of the lung for carbon monoxide (DLCO) \< 35% and/or receiving supplemental continuous oxygen * Liver abnormalities: fulminant liver failure, cirrhosis of the liver with evidence of portal hypertension, alcoholic hepatitis, esophageal varices, hepatic encephalopathy, uncorrectable hepatic synthetic dysfunction as evidenced 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 or symptomatic biliary disease * Human immunodeficiency virus (HIV)-positive patients * Women of childbearing potential who are pregnant (beta-HCG+) or breast feeding * Fertile men and women unwilling to use contraceptives during and for 12 months post-transplant * Life expectancy severely limited by diseases other than malignancy * DONOR: Donor-recipient pairs in which the HLA-mismatch is only in the HVG direction * DONOR: Cross-match positive with recipient