This pilot clinical trial studies the safety and maximum tolerated dose of brentuximab vedotin when given with tacrolimus and methotrexate after unrelated allogeneic donor stem cell transplant in patients with acute myeloid leukemia, acute lymphoblastic leukemia, or myelodysplastic syndromes. The addition of brentuximab vedotin to tacrolimus and methotrexate may result in a significant reduction of graft versus host disease in these patients.