Immunotherapy (Nivolumab or Brentuximab Vedotin) Plus Combination Chemotherapy in Treating Patients With Newly Diagnosed Stage III-IV Classic Hodgkin Lymphoma

Inclusion Criteria: * All patients must have histologically confirmed newly diagnosed, previously untreated stage III or IV classical Hodgkin lymphoma (nodular sclerosing, mixed cellularity, lymphocyte-rich, or lymphocyte-depleted, or not otherwise specified \[NOS\]). Nodular lymphocyte predominant Hodgkin lymphoma is not eligible. * Patients must have bidimensionally measurable disease (at least one lesion with longest diameter \>= 1.5 cm) documented on the Lymphoma Baseline Tumor Assessment Form in Rave. * Patients must have a whole body or limited whole body PET-CT scan performed within 42 days prior to registration. (A contrast-enhanced \[diagnostic\] CT, MRI or MR-PET is acceptable in event that PET-CT is contra-indicated, however if it is later possible to administer a PET-CT, then PET-CT is strongly preferred for the interim scan (after cycle 2) (if performed) and the EOT assessment. Otherwise, if PET-CT is not subsequently possible, then the same modality as baseline must be used throughout the trial.) NOTE: All images from PET-CT, CT, MRI or MR-PET scans performed as standard of care to assess disease (within 42 days prior to registration) must be submitted and associated radiology reports must be submitted. * Patients must be \>= 12 years of age. * Patients must not have received any prior chemotherapy, radiation, or antibody-based treatment for classical Hodgkin lymphoma. Steroid pre-treatment is permitted. * Patients must not have had prior solid organ transplant…