Visilizumab for the Prevention of Graft-versus-Host Disease After Allogeneic Hematopoietic Cell Transplantation

Inclusion Criteria: * One of the following diagnoses with histological confirmation by the Pathology Department at H. Lee Moffitt Cancer Center: * Acute Lymphocytic Leukemia (ALL) in complete remission 1 (CR1) with t(9:22) or t(4:11), or any ALL beyond CR1 * Acute Myelogenous Leukemia (AML) with high risk cytogenetics in CR1 as defined by Bloomfield any AML beyond CR1 * Myelodysplastic Syndrome (MDS) with International Prognostic Scoring System (IPSS) score \> 1 * Chronic myelomonocytic leukemia (CMML) * Chronic Myelogenous Leukemia (CML) with Imatinib-refractory chronic phase, or beyond chronic phase by morphology or cytogenetics * Myelofibrosis * Severe aplastic anemia * Chemosensitive Non-Hodgkin's lymphoma and Hodgkin's disease that are not candidate to autologous transplant due to prior autologous transplantation * Multiple Myeloma patient not candidate for autologous stem cell transplantation * Karnofsky performance status ≥ 70% (adult) * Normal organ and marrow function as defined below: * Hepatic: Total bilirubin must be less than or equal to 2mg/dL (Gilbert and other syndromes with increased indirect bilirubin are allowed); serum transaminases must be less than two times the upper limit of normal * Pulmonary: diffusing capacity of lung for carbon monoxide (DLCO) (corrected for Hgb), forced expiratory volume-one second (FEV1), forced vital capacity (FVC) must be greater than 50% predicted * Cardiac: Left ventricular ejection fraction at rest must be greater than 50% * Renal: Creatinine clearance (measured or calculated) must be equal or greater than 50 ml/min/1.73m\^2 Exclusion Criteria: * Anti thymocyte globulin (ATG) or anti T cell therapy in prior 45 days * Splenectomized patients; * A positive pregnancy test administered to all females of childbearing potential prior to allogeneic stem cell transplant * Inability to comply with follow up as determined by the patient's physician * HIV-I/II infection prior to hematopoietic stem cell (HSC) transplantation, confirmed by nucleic acid test (NAT) * Uncontrolled bacterial or fungal infection * History of documented invasive aspergillosis or cytomegalovirus (CMV) pneumonia * Presence of any of the following comorbid conditions: * History of myocardial infarction * Congestive heart failure (even if symptomatically controlled) * Peripheral vascular disease (including intermittent claudication or history of bypass for arterial insufficiency) * Untreated thoracic or abdominal aneurysm (6cm or more) * History of any cerebrovascular accident including transient ischemic attacks * Dementia * History of peptic ulcer disease requiring treatment * Connective tissue/rheumatologic disorders * Diabetes unless being managed with dietary changes only * Hemiplegia/paraplegia * History of solid tumor excluding skin or cervical carcinoma after curative resection