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 clearance must be \>= 60 mL/minute * Absolute neutrophil count (ANC) \>= 1000/uL * Platelets \>= 75,000/uL unless related to bone marrow involvement by HIV-cHL * Total bilirubin must be \< 1.5 x the upper limit of normal, unless the elevation of bilirubin is thought to be secondary to Gilbert's syndrome or combined antiretroviral therapy (cART); if, however, the elevated bilirubin is felt to be secondary to antiretroviral therapy, the total bilirubin must be =\< 3.5 mg/dL, provided that the direct bilirubin is normal and the aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x the upper limit of normal; also, if the elevated bilirubin is thought to be secondary to cHL the same criteria for hyperbilirubinemia should be applied; however 1 prior cycle of cyclophosphamide is permitted in attempt to make the participant eligible; patients should not be excluded from study participation unless dosing cannot be safely established * Female participants must have a negative pregnancy test within 1 week of enrollment and all participants must agree to use two reliable methods of contraception simultaneously if conception is possible during the study and for 6 months after stopping treatment; should a woman subject become pregnant or suspect she is pregnant while the subject is participating in this study, she should inform her treating physician immediately; the participant will then be removed from protocol therapy; participants who father a child while participating in the study will be permitted to continue with the protocol; the participant, however, is required to notify the investigator if he fathers a child * Ability to understand and the willingness to sign a written informed consent document * Karnofsky performance status \> 30% (given the aggressiveness of this disease and the often severely debilitated nature of the patients at initial presentation) * Measurable or non-measurable (evaluable) tumor parameter(s); non-measurable tumor parameters will be defined as not having bi-dimensional measurements (i.e., gastric or marrow involvement) but can be followed for response by other diagnostic tests such as gallium, PET imaging and/or bone marrow biopsy * Patients already receiving erythropoietin or granulocyte colony stimulating factor (GCSF) for treatment of HIV-related cytopenia are eligible * CD4 count \>= 50 cells/ul * Participants are required to be on antiretroviral regimens that are in accordance with the current International Acquired Immune Deficiency Syndrome (AIDS) Society guidelines concurrently with chemotherapy; the specific agents are at the discretion of the investigator and the use of investigational agents currently available on an expanded access basis is allowed; use of experimental antiretroviral agents or those containing zidovudine (including Combivir and Trizivir) or ritonavir (includes Norvir or Kaletra), cobicistat, didanosine (Videx or Videx EC), or similar potent cytochrome P450 (CYP)3 inhibitors are prohibited; in order to be eligible, participants taking zidovudine or ritonavir, or cobicistat, didanosine, or other CYP3 inhibitors must change to a different regimen 7 days prior to therapy initiation; changes to HAART therapy during the study may be made if medically necessary (toxicity, failure of regimen, etc.); participants must be on HAART at least 7 days prior to therapy * Negative for hepatitis B, or if infected with hepatitis B, receiving anti-hepatitis B therapy; all participants will be required to be screened for hepatitis B; per Infectious Disease Society of America (IDSA) and Assistance for AIDS Specific Drugs (AASD) guidelines, those participants that show no immunity, defined by the lack of hepatitis B surface antigen antibody, and show evidence of chronic infection (i.e. hepatitis B surface antigen \[HBsAg\]+, hepatitis B core \[HBcore\]+, hepatitis B surface antibody \[HBsAB\]-) will be required to be on anti-hepatitis B therapy during the study in order to be eligible; patients will be permitted to enroll in the study provided normal liver function tests and no evidence of cirrhosis; the exact hepatitis B therapy will be at the discretion of the infection disease specialist or investigator; however all patients who present with acute hepatitis B or show normal transaminases and are hepatitis B virus HBsAg surface protein antigen (HBsAg) positive (+) and immunoglobulin M (IgM)+ for hepatitis core antigen will not be eligible for trial enrollment * Patients diagnosed with hepatitis C who are hepatitis C antibody positive, whether hepatitis C RNA level is measurable or not, must have no evidence of cirrhosis and have liver function tests * Brentuximab vedotin is partially metabolized via the CYP3A4 pathway and is cleared from the cells via the P-glycoprotein pump; therefore, participants must discontinue use of the following agents within 7 days prior to therapy * Strong CYP3A4 inhibitors that treat HIV * Other strong CYP3A inhibitors * Moderate CYP3A4 inhibitors should be used with caution but are not excluded; if 2 moderate CYP3A4 inhibitors are used concurrently, one must be discontinued at least 7 days (1 week) prior to the initiation of chemotherapy * P-glycoprotein inhibitors * If patients are taking any of these excluded medications, they must be discontinued at least 7 days (1 week) prior to the initiation of chemotherapy All concomitant medications must be reviewed by the study chair or co-chair prior to enrollment by email; because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference for a list of drugs to avoid or minimize use of Exclusion Criteria: * Patients with prior anthracycline therapy will be excluded * Female participants who are pregnant or breast-feeding; confirmation that the subject is not pregnant must be established by a negative serum beta (b)-human chorionic gonadotropin (b-hCG) or urine pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women * Medical illness unrelated to HL, which in the opinion of the study physician will preclude administration of chemotherapy safely; this includes patients with uncontrolled infection (including opportunistic), chronic renal failure, myocardial infarction (MI) within the past 6 months, unstable angina, or cardiac arrhythmias other than chronic atrial fibrillation, or second malignancy requiring active treatment * Prior malignancy within 2 years before enrollment other than curatively treated cutaneous basal cell or squamous cell carcinoma, carcinoma in situ of the cervix, anal intraepithelial neoplasia, or cutaneous Kaposi's sarcoma (KS); participants with prior malignancies must have completed all therapy at least 2 years before enrollment with no evidence of disease since therapy completion * Grade 2 or greater peripheral neuropathy * Evidence of progressive multifocal leukoencephalopathy (PML) identified on the pretreatment magnetic resonance imaging (MRI) * Central nervous system disease * Patients with history of John Cunningham (JC) virus identified in the cerebrospinal fluid (CSF) or previous history of PML will be excluded from the study * Cirrhosis secondary to any cause will be excluded