Brentuximab Vedotin Prevention of (GVHD) After Unrelated Allogeneic Stem Cell Transplantation

Inclusion Criteria: * Patient must be scheduled to undergo stem cell transplantation for one of the following diagnoses: * acute myeloid leukemia (AML) in CR1 (first complete remission, CR or CRi) or CR2 (second complete remission, CR or CRi), * acute lymphoblastic leukemia (ALL) in CR1 or CR2 (CR or CRi) * myelodysplastic syndrome (MDS) without progression to AML. * Chronic myelogenous leukemia (CML) * Non-Hodgkin's lymphoma (NHL) or Hodgkin's disease (HD) * Chronic lymphocytic leukemia (CLL) * Multiple myeloma (MM) * Patients must be the recipient of unrelated donor peripheral blood stem cell products. Mismatches at both antigen and allele level will be eligible. Match must be 6 or 7 out of 8 loci (HLA A, B, C, and DRB1). * Patient must receive any one of the following conditioning regimens: total body radiation (single or fractionated dose)/cyclophosphamide, busulfan/ cyclophosphamide, or fludarabine/busulfan/lymphocyte immune globulin (ATGAM/thymo). * Patient must be ≥ 18 years and ≤ 70 years of age. * Patient must have an ECOG performance status ≤ 2 or Karnofsky performance scale ≥ 60% * Patient must have CD34+ stem cells ≥ 2x106/kg (actual body weight of the recipient) available for transplantation. * Patient must have appropriate organ function as defined below (this criterion should be met on screening and on the day of the first dose of brentuximab vedotin (as assessed prior to dosing)): * Total bilirubin ≤ 2.0 x IULN * AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN * Serum creatinine ≤ 2.0 x IULN * Estimated Creatinine Clearance \> 30 ml/min * Cardiac ejection fraction \> 40% * DLCO/VA \> 40% * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Patient must be able to understand and willing to sign an IRB approved written informed consent document. Exclusion Criteria: * Patient must not have had prior exposure to brentuximab vedotin. * Patient must not have a history of other malignancy that has not been in remission for at least 3 years, with the exception of basal non-melanoma skin cancer which were treated with local resection only or intraepithelial lesions or carcinoma in situ of the cervix or prostate that has been curatively treated. * Patient must not be receiving any other investigational agents. * Patient must not have active CNS involvement. * Patient must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to brentuximab vedotin or other agents used in the study. * Patients must not have had previous radiation therapy to the mediastinum or lungs. * Patient must not have an uncontrolled inter-current illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, active pulmonary diseases, or psychiatric illness/social situations that would limit compliance with study requirements (this criterion should be met on screening and on the day of but prior to first dose of brentuximab vedotin). * Patient must not be pregnant and/or breastfeeding. * Patient must not be known to be HIV-positive on combination antiretroviral therapies. * Patient must not have had a previous allogeneic or syngeneic transplant. Prior autologous transplant is allowed.