Brentuximab Vedotin or Crizotinib and Combination Chemotherapy in Treating Patients With Newly Diagnosed Stage II-IV Anaplastic Large Cell Lymphoma

Inclusion Criteria: * Newly diagnosed patients with histologically proven ALCL (International Classification of Diseases for Oncology \[ICD-0\] code: 9714/3) * Disease must be cluster of differentiation (CD)30 positive * Disease must be anaplastic lymphoma kinase (ALK) positive (defined by local institutional standards) * Patients must have stage II, III, or IV disease * Patients must have a life expectancy of \>= 8 weeks * Adequate Liver Function Defined As: * Total bilirubin =\< 1.5 x upper limit of normal (ULN) for age (within 7 days prior to enrollment) * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 x upper limit of normal (ULN) for age; for the purpose of this study, the ULN for ALT is 45 U/L (within 7 days prior to enrollment) * If the lab abnormality is thought to be due to the lymphoma the patient is eligible and dose adjustments should be made * Adequate Cardiac Function Defined As: * Shortening fraction of \>= 27% by echocardiogram, or * Ejection fraction of \>= 50% by radionuclide angiogram * Adequate Pulmonary Function Defined As: * Patients with a history of pulmonary dysfunction must have no evidence of dyspnea at rest, no exercise intolerance due to pulmonary insufficiency, and a pulse oximetry \> 92% while breathing room air unless current dysfunction is due to the lymphoma in which case the patient is eligible Exclusion Criteria: * Patients with central nervous system (CNS) disease are not eligible * Patients with …