Treating Relapsed/Recurrent/Refractory Pediatric Solid Tumors With Sorafenib in Combination With Irinotecan

Inclusion Criteria: * Greater than or equal to 24 months to 21 years of age * Relapsed, refractory, or recurrent malignancy. All solid tumor diagnoses will be eligible. * Pathologic confirmation of the diagnosis either at original diagnosis or recurrence. * Known non-synonymous mutation in the following genes: Raf, PDGFR, VEGFR, Flt-3, KIT, JAK, STAT, RAS, MEK, or ERK. Genomic sample preferably from relapse, but may be from other stage of treatment if relapse sample is not reasonably obtainable. Genetic analysis for determination of eligibility occurs as part of routine care and is not being performed specifically for the purposes of this study. * Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with CT or MRI scan, as ≥ 20 mm by chest x-ray, or ≥ 10 mm with calipers by clinical exam. * Prior Therapy * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study. * Myelosuppressive chemotherapy: Patients must not have received myelosuppressive chemotherapy within 2 weeks of enrollment onto this study (6 weeks if prior nitrosourea). * Hematopoietic growth factors: At least 14 days must have elapsed after receiving pegfilgrastim and least 7 days must have elapsed since the completion of therapy with a non-pegylated growth factor. * Biologic (anti-neoplastic agent): At least 7 days must have elapsed since completion of therapy with a biologic agent. For agents that have known adverse events occurring beyond 7 days after administration, this period prior to enrollment must be extended beyond the time during which adverse events are known to occur. * Monoclonal antibodies: At least 3 half-lives must have elapsed since prior therapy that included a monoclonal antibody. (See posting of half-lives for commonly used monoclonal antibodies on the DVL homepage; https://members.childrensoncologygroup.org/Disc/devtherapeutics/default.asp.) * Radiotherapy: ≥ 2 weeks must have elapsed since local palliative XRT (small port); ≥ 6 weeks must have elapsed since treatment with therapeutic doses of MIBG; ≥ 3 months must have elapsed if prior craniospinal XRT was received, if ≥ 50% of the pelvis was irradiated, or if TBI was received; ≥ 6 weeks must have elapsed if other substantial bone marrow irradiation was given. * Stem Cell Transplant or Rescue without TBI: No evidence of active graft vs. host disease and ≥ 2 months must have elapsed since transplant. * Patients must have a performance status corresponding to Karnofsky or Lansky greater than or equal to 50%. Use Karnofsky for patients \> 16 years of age and Lansky for patients ≤ 16 years of age. 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. * Normal bone marrow and organ function as defined below: * Absolute neutrophil count ≥ 1,000/mcl * Platelets ≥ 75,000/mcl (transfusion independent, defined as not receiving platelet transfusions within a 7 day period prior to enrollment) * Total bilirubin ≤ IULN * AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN Note: For the purposes of this trial the ULN for ALT is defined as 45 U/L. * Adequate Renal Function Defined As: Creatinine clearance or radioisotope GFR \> 70 mL/min/1.73 m2 or a serum creatinine based on age/gender as follows: 2 to \< 6 years (male=0.8, female=0.8), 6 to \<10 years (male=1, female=1), 10 to \< 13 years (male=1.2, female=1.2), 13 to \< 16 years (male=1.5, female=1.4), and ≥ 16 years (male=1.7, female=1.4) * PTT \< IULN * INR \< IULN or PT \< IULN * Normal serum lipase and amylase (per institutional normal values). * Adequate Pulmonary Function Defined As: No evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry \> 94%. * Adequate cardiovascular functioning for sorafenib, including: * Shortening fraction ≥ 28% or ejection fraction (LVEF) ≥ 55%, as well as * A blood pressure (BP) ≤ the 95th percentile for age, height, and gender and not receiving medication for treatment of hypertension. * Normal electrocardiogram with QTc \< 450. * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Exclusion Criteria: * Patients who have received a cumulative doxorubicin equivalent of \> 375mg/m\^2 total lifetime dose. * Surgery Criteria: Patients who have had or are planning to have the following invasive procedures are not eligible: * Major surgical procedure, laparoscopic procedure, open biopsy or significant traumatic injury within 14 days prior to initiation of protocol therapy. There should be no anticipation of need for major surgical procedures during the course of the study. * Central line placement or subcutaneous port placement is not considered major surgery. External central lines must be placed at least 3 days prior to initiation of protocol therapy and subcutaneous ports must be placed at least 7 prior to initiation of protocol therapy * Patients must not be on therapeutic anti-coagulation. Prophylactic anticoagulation (i.e. low dose warfarin) of venous or arterial devices is allowed provided that the requirements for PT, INR, and PTT are met. * Patients with evidence of bleeding diathesis are not eligible. * Patients with known Gilbert syndrome are not eligible. * A history of other malignancy ≤ 5 years previous with the exception of basal cell or squamous cell carcinoma of the skin which were treated with local resection only or carcinoma in situ of the cervix. * Currently receiving any other investigational agents. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to sorafenib or irinotecan. * Currently on the following concomitant medications or substances that have the potential to affect the activity or pharmacokinetics of the study drug(s). The use of the following medications should be discontinued prior to initiation of protocol therapy and should be avoided during protocol therapy if reasonable alternatives exist. * Sorafenib * Irinotecan * Corticosteroids: Patients requiring corticosteroids that have not been on a stable or decreasing dose of corticosteroid for 7 days prior to enrollment are not eligible. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, cardiac dysfunction, unstable angina pectoris, cardiac arrhythmia, prolonged QTc, interstitial lung disease, gastrointestinal perforation, hepatic impairment/failure, or renal impairment/failure. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative serum or urine pregnancy test within 7 days of study entry. * Known HIV-positivity on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with sorafenib or irinotecan. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.