Crizotinib and Combination Chemotherapy in Treating Younger Patients With Relapsed or Refractory Solid Tumors or Anaplastic Large Cell Lymphoma

Inclusion Criteria: * Patients must have had histologic verification of malignancy at original diagnosis or relapse; all patients with relapsed or refractory solid tumors or anaplastic large cell lymphoma (ALCL) are eligible except for patients with primary or metastatic central nervous system (CNS) tumors or patients with primary cutaneous ALCL * Patients must have either measurable or evaluable disease * Patients current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 60% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age; Note: patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must have fully recovered from the acute toxic effects of all prior anti-cancer chemotherapy * Myelosuppressive chemotherapy: * Solid tumors: at least 21 days after the last dose of myelosuppressive chemotherapy (42 days if prior nitrosourea) * ALCL: * Patients with ALCL who relapse while receiving standard maintenance chemotherapy will not be required to have a waiting period before enrollment onto this study * Patients who relapse while they are not receiving standard maintenance therapy, must have fully recovered from all acute toxic effects of prior therapy; at least 14 days must have elapsed after the c…