Brentuximab Vedotin in High-Risk CD30+ Lymphoma Post Allogeneic Stem Cell Transplantation (AlloSCT)

Study Drug Administration: If you agree to take part in this study, about 35-60 days after the transplant, you will receive brentuximab vedotin by vein over about 30 minutes on Day 1 of each 21-day study cycle. You may receive up to 6 cycles of brentuximab vedotin. At Cycles 3 and beyond, you will receive a higher dose of the study drug than you received during Cycles 1 and 2. Study Visits: About 5 days before Day 1 of Cycle 1: * You will have a physical exam. As part of the physical exam, you will be checked for graft-versus-host disease (GVHD -- when transplanted donor tissue attacks the tissues of the recipient's body). You may have an additional blood draw to check for GVHD as part of your standard of care. * Blood (about 2 tablespoons) will be drawn for routine tests and to check how the transplant has taken. * Blood (about 2 teaspoons each time) will be drawn before and after your dose of study drug to check the immune system. On Days 3 and 5 of Cycle 1, blood (about 2 teaspoons) will be drawn to check the immune system. About 5 days before Day 1 of Cycles 2-6: * You will have a physical exam. * Blood (about 2 tablespoons) will be drawn for routine tests and to check the immune system. If your doctor thinks it is needed, you may have a skin biopsy or endoscopy to check for GVHD and/or graft failure. You will sign a separate consent form that explains the procedures and risks. Length of Study: You will be taken off study 1 year after the transplant. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, if you develop an infection (such as cytomegalovirus \[CMV\] that does not respond to treatment), or if you are unable to follow study directions. Your participation on the study will be over after the follow-up visits. Follow-Up Visits: About 1, 3, 6, and 12 months after the transplant, you will have follow-up visits as part of your standard of care after your transplant. At these visits: * You will have a physical exam * Blood (about 4 tablespoons) will be drawn for routine tests, to learn how the transplant has taken, and to check the status of the disease. * You will have a computed tomography (CT) scan to check the status of the disease. * You will have a bone marrow biopsy and aspiration to check the status of the disease and for cytogenetic testing. To collect a bone marrow biopsy/aspirate, an area of the hip or other site is numbed with anesthetic, and a small amount of bone marrow and bone is withdrawn through a large needle. Cytogenetic testing looks at how genetic changes to cells may affect how the disease may react to the study drug. This is an investigational study. Brentuximab vedotin is FDA approved and commercially available for the treatment of Hodgkin lymphoma and ALCL. It is investigational to give brentuximab vedotin at an earlier time after a transplant. Up to 20 participants will be enrolled in this study. All will take part at MD Anderson.