Brentuximab Vedotin, Ifosfamide, Carboplatin, and Etoposide in Treating Patients With Relapsed or Refractory Hodgkin Lymphoma

Inclusion Criteria: * Patients must have primary refractory or first relapse of cluster of differentiation 30 (CD30)+ Hodgkin lymphoma * Patients must have measurable disease defined as lesions that can be accurately measured in two dimensions by computed tomography (CT), magnetic resonance imaging (MRI), medical photograph (skin or oral lesion), plain x-ray, or other conventional technique and a greatest transverse diameter of 1 cm or greater; or palpable lesions with both diameters \>= 2 cm; further, at least 1 of these lesions must be positive by positron emission tomography (PET) scan (i.e., Deauville score of 4 or more); Note: CT scans remain the standard for evaluation of nodal disease * Patients must have a CT of chest, abdomen, and pelvis with PET within 28 days of enrollment; patients with evidence of lymphadenopathy in the neck must have a dedicated CT of neck * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (performance status of 2 will be allowed if poor performance status is thought to be directly secondary to patient's Hodgkin lymphoma \[HL\]) * Absolute neutrophil count (ANC) \>= 1,500/uL, performed within 28 days prior to registration * Platelets \>= 100,000/uL (without transfusion or growth factor support), performed within 28 days prior to registration * Serum creatinine \< 1.5 mg/dl or creatinine clearance (CrCl) \> 60 mL/min, performed within 28 days prior to registration * Total bilirubin \< 2 times upper lim…