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 completion of cytotoxic therapy * Hematopoietic growth factors: at least 14 days after the last dose of a long-acting growth factor (e.g. Neulasta) or 7 days for short-acting growth factor; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * Biologic (anti-neoplastic agent): at least 7 days after the last dose of a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * Immunotherapy: at least 42 days after the completion of any type of immunotherapy, e.g. tumor vaccines * Monoclonal antibodies: at least 3 half-lives of the antibody after the last dose of a monoclonal antibody * Radiation therapy (XRT): * Solid tumors: at least 14 days after local palliative XRT (small port); \>= 6 weeks must have elapsed since treatment with therapeutic doses of metaiodobenzylguanidine (MIBG); at least 150 days must have elapsed if prior total body irradiation (TBI), craniospinal XRT or if \>= 50% radiation of pelvis; at least 42 days must have elapsed if other substantial bone marrow (BM) radiation * ALCL: at least 14 days after local palliative XRT (small port); at least 84 days must have elapsed if prior TBI, craniospinal XRT or if \>= 50% radiation of pelvis; at least 42 days must have elapsed if other substantial BM radiation * Stem cell infusion without TBI: no evidence of active graft vs. host disease and at least 84 days must have elapsed after transplant and \>= 42 days for autologous stem cell infusion after iodine (I)131-MIBG therapy * Patients must not have received prior therapy with crizotinib * Prior anthracycline dose: patients with a total lifetime cumulative anthracycline dose of \> 650 mg/m\^2 at the time of enrollment are not eligible for Part B of the study * For patients with solid tumors or ALCL without known bone marrow involvement: * Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * Patients with known bone marrow metastatic disease will be eligible for study provided they meet the blood counts (may receive transfusions provided they are not known to be refractory to red cell or platelet transfusions); these patients will not be evaluable for hematologic toxicity; if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 ml/min/1.73 m\^2 or a serum creatinine based on age/gender as follows: * Age 1 to \< 2 years: 0.6 mg/dL * Age 2 to \< 6 years: 0.8 mg/dL * Age 6 to \< 10 years: 1 mg/dL * Age 10 to \< 13 years: 1.2 mg/dL * Age 13 to \< 16 years: 1.5 mg/dL (males) and 1.4 mg/dL (females) * Age \>= 16 years: 1.7 mg/dL (males) and 1.4 mg/dL (females) * Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 110 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * Corrected QT interval (QTc) =\< 480 msec * For patients on Part B: shortening fraction of \>= 27% by echocardiogram or ejection fraction of \>= 50% by gated radionuclide study * All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines * Part C: Patients must have a body surface area (BSA) \>= 1.07 m\^2 at the time of study enrollment * Part D: Patients must have a body surface area (BSA) \>= 0.43 m\^2 at the time of study enrollment * Tumor tissue must be sent; if tumor tissue is unavailable, the study chair must be notified prior to enrollment Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study; pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method during treatment and for 3 months after stopping treatment * Patients receiving corticosteroids who have not been on a stable or decreasing dose of corticosteroid for at least 7 days prior to enrollment are not eligible * Patients who are currently receiving another investigational drug are not eligible * Patients who are currently receiving other anti-cancer agents are not eligible * Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial * Patients chronically receiving medications known to be metabolized by cytochrome P 450, family 3, subfamily A, polypeptide 4 (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 * Patients chronically receiving drugs that are known potent CYP3A4 inhibitors within 7 days prior to study enrollment, including but not limited to ketoconazole, itraconazole, miconazole, clarithromycin, erythromycin, ritonavir, indinavir, nelfinavir, saquinavir, amprenavir, 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 * 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, tipranavir, ritonavir, and St. John?s wort are not eligible; the topical use of these medications (if applicable) is allowed * Patients receiving PPIs and H2 blockers are not eligible for Part D * Patients who have an uncontrolled infection are not eligible * Patients who have received a prior solid organ transplantation are not eligible * Patients who have a primary or metastatic CNS tumor at the time of study enrollment are not eligible; a prior history of metastatic CNS tumor is allowed as long as there is no evidence of CNS disease at study enrollment * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible * Parts A and B: Patients who are able to swallow liquid or use a nasogastric or gastrostomy (G) tube are eligible * Part C: Patients must be able to swallow intact capsules * Part D: Patients must be able to swallow liquid