Donor Stem Cell Transplant in Treating Patients With Hematologic Cancer or Other Diseases

Inclusion Criteria: * Histologically confirmed hematological disease, including any of the following: * Chronic lymphocytic leukemia * Absolute lymphocytosis \> 5,000/µL * Morphologically mature lymphocytes with \< 55% prolymphocytes * Lymphocyte phenotype with expression of CD19 and CD5 * Absence of CD23 expression allowed provided disease is morphologically distinguished from mantle cell lymphoma * Prolymphocytic leukemia * Absolute lymphocytosis \> 5,000/µL * Morphologically mature lymphocytes with \> 55% prolymphocytes * Non-Hodgkin's or Hodgkin's lymphoma * Any WHO classification histologic subtype * Diagnosis by core biopsy allowed provided there is adequate tissue for diagnosis and immunophenotyping * Diagnosis by bone marrow biopsy not acceptable for follicular lymphomas * Multiple myeloma * Has received ≥ 1 prior treatment regimen * Has a partial response or greater by the Blade Criteria * Patients who achieved complete remission are eligible * Acute myeloid leukemia * Documented control (i.e., \< 10% bone marrow blasts and no circulating blasts) * Myelodysplastic syndromes * Documented disease as defined by WHO or French-American-British Cooperative group criteria * Chronic myelogenous leukemia * Patients with atypical chronic myelogenous leukemia (i.e., absent Philadelphia chromosome) are eligible * Polycythemia vera * Documented disease as defined by WHO criteria (i.e., A1 + A2, and any other category A, OR A1 + A2, and any 2 category B): * A1: Total red blood cell mass \> 25% above mean normal predicted value OR hemoglobin \> 18.5 g/dL in males, 16.5 g/dL in females (hematocrit ≥ 60% in males or ≥ 56% in females) * A2: No cause of secondary erythrocytosis (absence of familial erythrocytosis, no elevation of epoetin alfa \[EPO\] due to hypoxia, high oxygen affinity hemoglobin, truncated EPO receptor, or inappropriate ectopic EPO production) * A3: Splenomegaly * A4: Clonal genetic abnormality other than the Philadelphia chromosome * A5: Endogenous erythroid colony formation in vitro * B: Platelet count \> 400,000/mm³, WBC \> 12,000/mm³, bone marrow biopsy with prominent erythroid and megakaryocytic proliferation, and low serum EPO * Chronic idiopathic myelofibrosis * Documented disease as defined by WHO criteria * Must have a HLA-identical donor, a matched unrelated donor, or a HLA 9/10 related donor meeting the following criteria: * HLA-identical sibling (6/6) * Serologic typing for class I (A, B) * Molecular typing for class II (DRB1) * 9/10 matched related donor * High-resolution molecular typing at HLA-A, B, C, DRB1, and DQB1 * Only a single mismatch at one class I or II allele allowed * 10/10 matched unrelated donor * Molecular identity at HLA-A, B, C, DRB1, and DQB1 by high-resolution typing * Syngeneic donors are not eligible * Creatinine clearance ≥ 40 mL/min * Bilirubin ≤ 3 times upper limit of normal (ULN) * AST ≤ 3 times ULN * DLCO ≥ 40% with no symptomatic pulmonary disease * LVEF ≥ 30% by cardiac MRI or echocardiogram with no symptomatic cardiac disease * Fertile patients willing to use effective contraception Exclusion Criteria: * Uncontrolled diabetes mellitus * Active serious infection * Known hypersensitivity to E. coli-derived products * Known HIV positivity * History of another malignancy\*, meeting the following criteria: * Non-skin malignancy or melanoma within the past 5 years * Concomitant malignancy that has not been curatively treated * NOTE: \*However, cancer survivors who have undergone potentially curative therapy for a prior malignancy at least 5 years before enrollment and are deemed at low risk of \< 30% for recurrence by their treating physicians is considered * Pregnant or nursing