This partially randomized phase II trial studies how well brentuximab vedotin or crizotinib and combination chemotherapy works in treating patients with newly diagnosed stage II-IV anaplastic large cell lymphoma. Brentuximab vedotin is a monoclonal antibody, called brentuximab, linked to a toxic agent called vedotin. Brentuximab attaches to CD30 positive cancer cells in targeted way and delivers vedotin to kill them. Crizotinib and methotrexate may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. It is not yet known whether brentuximab vedotin and combination chemotherapy is more effective than crizotinib and combination chemotherapy in treating anaplastic large cell lymphoma.

PRIMARY OBJECTIVES:

I. To determine the tolerability of brentuximab vedotin given in combination with standard chemotherapy (anaplastic large cell lymphoma [ALCL]99) and to determine the tolerability of crizotinib given in combination with chemotherapy (ALCL99).

II. To estimate the event free survival (EFS) of Arm brentuximab vedotin (BV) and Arm crizotinib (CZ) and contrast these to historical control data.

SECONDARY OBJECTIVES:

I. To determine the prognostic significance of minimal disseminated disease (MDD) at diagnosis and minimal residual disease (MRD) as measured by real-time (RT)-polymerase chain reaction (PCR) in peripheral blood.

OUTLINE: Patients with body surface area (BSA) < 0.9 m^2 were non-randomly assigned to Arm BV while it was open and were not eligible for the trial while Arm BV was closed. Patients with BSA >= 0.9 m^2 were randomly assigned 1:1 to Arm BV or Arm CZ while both were open and were non-randomly assigned to the open arm while only one of the two arms was open.

ARM BV:

COURSE A (CYCLES 1, 3, AND 5): Patients receive brentuximab vedotin (1.8 mg/dg/dose - Max dose 180 mg) intravenously (IV) over 30 minutes on day 1, dexamethasone orally (PO) twice daily (BID) or IV on days 1-5, ifosfamide IV over 60 minutes on days 1-5, methotrexate IV over 3 hours on day 1, cytarabine IV over 1-30 minutes every 12 hours for 4 doses on days 4 and 5, and etoposide IV over 2 hours on days 4 and 5.

COURSE B (CYCLES 2, 4, AND 6): Patients receive brentuximab vedotin (1.8 mg/dg/dose - Max dose 180 mg), dexamethasone, and methotrexate as in Arm BV, Course A. Patients also receive cyclophosphamide IV over 15-30 minutes on days 1-5 and doxorubicin hydrochloride IV over 1-15 minutes on days 4 and 5.

ARM CZ:

COURSE A (CYCLES 1, 3, AND 5): Patients receive crizotinib (165 mg/m^2) PO BID on days 1-21 and dexamethasone, ifosfamide, methotrexate, cytarabine, and etoposide as in Arm BV, Course A.

COURSE B (CYCLES 2, 4, AND 6): Patients receive crizotinib (165 mg/m^2) PO BID as in Arm CZ, Course A and dexamethasone, cyclophosphamide, methotrexate, and doxorubicin hydrochloride as in Arm BV, Course B.

In all arms, treatment repeats every 21 days for 6 cycles in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 3, 6, 9, 12, 18, 24, 36, 48, and 60 months.

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