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 (HL)
* For children who are unable to cooperate for PFTs, the criteria are: no evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry reading of \> 92% on room air
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met

Exclusion Criteria:

* Patients with nodular lymphocyte-predominant HL
* Patients with an immunodeficiency that existed prior to diagnosis, such as primary immunodeficiency syndromes, organ transplant recipients and children on current systemic immunosuppressive agents are not eligible
* Patients who are pregnant; (since fetal toxicities and teratogenic effects have been noted for several of the study drugs, a negative pregnancy test is required for female patients of childbearing potential)
* Lactating females who plan to breastfeed
* Sexually active patients of reproductive potential who have not agreed to use an effective contraceptive method for the duration of their study participation and for 30 days after the last dose of chemotherapy
* Patients known to be positive for human immunodeficiency virus (HIV) are not eligible
* Patients who have received any previous chemotherapy or radiation therapy are not eligible
* Patients who received systemic corticosteroids within 28 days of enrollment on this protocol, except as specified, are not eligible