Brentuximab Vedotin Before Autologous Stem Cell Transplant in Treating Patients With Hodgkin Lymphoma

PRIMARY OBJECTIVES: I. The primary objective of this study is to determine the activity of salvage brentuximab vedotin in Hodgkin lymphoma prior to autologous hematopoietic stem cell transplantation, as measured by overall response rate (ORR). SECONDARY OBJECTIVES: I. To describe the safety, toxicity, and tolerability of brentuximab vedotin as a salvage regimen. II. To summarize the stem cell mobilization results of patients receiving brentuximab vedotin as salvage therapy (e.g., total cluster of differentiation (CD)34+ cell yield, number of apheresis days, proportion of patients who achieve \>= 3 x 10\^6 CD34+ cells/kg). III. To evaluate potential changes in Hodgkin lymphoma biological markers of patients treated with brentuximab vedotin as first line salvage therapy. IV. To examine and characterize the outcomes of patients who receive brentuximab vedotin as first line salvage followed by autologous hematopoietic stem cell transplantation (AHCT) (e.g., toxicity, 2-year progression free survival \[PFS\], overall survival \[OS\], relapse-progression incidence and non-relapse mortality rate \[NRM\]) OUTLINE: Patients receive brentuximab vedotin intravenously (IV) over 30 minutes on day 1. Treatment repeats every 21 days for up to 4 courses. Patients in the new cohort receive regular study dose of brentuximab vedotin for courses 1 and 2. Patients not achieving complete remission (CR) after 2 courses receive higher-dose brentuximab vedotin IV over 60 minutes on day 1 for 2 additional courses. After completion of study treatment, patients are followed up at 21 days.