Brentuximab Vedotin and Combination Chemotherapy in Treating Patients With Stage II-IV HIV-Associated Hodgkin Lymphoma

Inclusion Criteria: * HIV positive; documentation of HIV-1 infection by means of any one of the following: * Documentation of HIV diagnosis in the medical record by a licensed health care provider; * Documentation of receipt of antiretroviral therapy (ART) by a licensed health care provider; * HIV-1 RNA detection by a licensed HIV-1 RNA assay demonstrating \> 1000 RNA copies/mL; * Any licensed HIV screening antibody and/or HIV antibody/antigen combination assay confirmed by a second licensed HIV assay such as a HIV-1 western blot confirmation or HIV rapid multispot antibody differentiation assay * NOTE: A "licensed" assay refers to a United States (US) Food and Drug Administration (FDA)-approved assay, which is required for all investigational new drug (IND) studies * Histologic diagnosis of CD30-positive classical HL as defined by the 2008 World Health Organization (WHO) Classification of Hematological diseases; nodular lymphocyte predominant Hodgkin lymphoma is not eligible * Stage II, III or IV disease as defined by the Ann Arbor Staging System * Participants must have previously untreated HIV-classical HL (cHL), with the exception of up to 14 consecutive days of steroids, emergency radiation, or 1 prior cycle of cyclophosphamide to reduce tumor burden and improve hyperbilirubinemia in the setting of lymphoma related liver involvement * Normal baseline cardiac ejection fraction \>= 50% * Serum creatinine of =\< 1.5 mg/dL; if creatinine \> 1.5 mg/dL, creatinine …