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 disease limited to the skin are not eligible, regardless of how wide-spread * Patients with stage I disease are not eligible * Patients who have received any prior cytotoxic chemotherapy for the current diagnosis of ALCL or any cancer diagnosed previously are not eligible * Previous steroid treatment and/or radiation treatment is not allowed unless it is for the emergent management of a mediastinal mass; emergent steroid treatment and/or radiation treatment should stop once protocol therapy is initiated * Intrathecal chemotherapy prior to enrollment is allowed for the current diagnosis of ALCL as long as adequate cerebrospinal fluid (CSF) is obtained prior to administration of the intrathecal chemotherapy and subsequently demonstrated to be negative for ALCL * Female patients who are pregnant are not eligible; pregnancy tests must be obtained in girls who are post menarchal * Lactating females are not eligible unless they have agreed not to breastfeed their infants * Sexually active patients of reproductive potential are not eligible unless they agree to use an effective contraceptive method for the duration of treatment and for 3 months after stopping treatment * Patients with Down syndrome are not eligible due to the amount of methotrexate and potential for side effects * Patients with an immunodeficiency that existed prior to diagnosis such as primary immunodeficiency syndromes or organ transplant recipients are not eligible * Cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) substrates with narrow therapeutic indices: Patients chronically receiving medications known to be metabolized by CYP3A4 and with narrow therapeutic indices including pimozide, aripiprazole, triazolam, ergotamine and halofantrine are not eligible; the topical use of these medications (if applicable) is allowed * CYP3A4 inhibitors: patients chronically receiving drugs that are known potent CYP3A4 inhibitors within 7 days prior to study enrollment, including but not limited to ketoconazole, itraconazole, clarithromycin, erythromycin, ritonavir, indinavir, nelfinavir, saquinavir, delavirdine, nefazodone, diltiazem, verapamil, and grapefruit juice are not eligible; the topical use of these medications (if applicable), e.g. 2% ketoconazole cream, is allowed * CYP3A4 inducers: patients chronically receiving drugs that are known potent CYP3A4 inducers within 12 days prior to study enrollment, including but not limited to carbamazepine, phenobarbital, phenytoin, rifabutin, rifampin, ritonavir, and St. John's wort are not eligible; the topical use of these medications (if applicable) is allowed * Patients that are known to be positive for human immunodeficiency virus (HIV) are not eligible; note: inclusion of HIV positive patients will be considered at a later date * Patients who weigh \< 10 kg are not eligible