Brentuximab Vedotin and Combination Chemotherapy in Treating Children and Young Adults With Stage IIB, Stage IIIB, IVA, or IVB Hodgkin Lymphoma

Inclusion Criteria: * Patients with newly diagnosed, pathologically confirmed cHL meeting one of the following Ann Arbor stages are eligible: * Stage IIB with bulk * Stage IIIB * Stage IVA * Stage IVB * If study eligibility by staging is uncertain, consultation with Imaging and Radiation Oncology Core (IROC) Rhode Island (RI) may be obtained prior to study enrollment * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows (performed within 14 days prior to enrollment): * 2 to \< 6 years: male 0.8 mg/dL, female 0.8 mg/dL * 6 to \< 10 years: male 1 mg/dL, female 1 mg/dL * 10 to \< 13 years: male 1.2 mg/dL, female 1.2 mg/dL * 13 to \< 16 years: male 1.5 mg/dL, female 1.4 mg/dL * \>= 16 years: male 1.7 mg/dL, female 1.4 mg/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age (performed within 14 days prior to enrollment) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate transaminase \[AST\]) or serum glutamate pyruvate transaminase (SGPT) (alanine transaminase \[ALT\]) \< 2.5 x upper limit of normal (ULN) for age (performed within 14 days prior to enrollment) * Shortening fraction of \>= 27% by echocardiogram, or ejection fraction of \>= 50% by radionuclide angiogram * Forced expiratory volume in 1 second (FEV1)/forced vital capacity (FVC) \> 60% by pulmonary function test (PFT), unless due to large mediastinal mass from Hodgkin lymphoma (…