A Trial of Everolimus and Bevacizumab in Children With Recurrent Solid Tumors

Inclusion Criteria: * Diagnosis: Solid tumor, including central nervous tumors, that is recurrent or refractory to standard therapy or for which standard therapy is not available. All research participants must have a pathologic diagnosis either from their initial presentation, or at the time of recurrence or progression. The requirement for histologic verification may be waived for patients with brainstem glioma and optic pathway glioma. * Performance Status: Karnofsky \> 50% for \> 10 years of age; Lansky \> 50% for children \< 10 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 purposes of assessing performance score. * Neurologic deficits. Patients with CNS tumors must have stable neurological deficits for a minimum of 1 week prior to study entry. * Life Expectancy: Must be greater than 8 weeks. * Prior/Concurrent Therapy: Research participants must have recovered from the acute effects of prior treatment and: * Chemotherapy: Must not have received myelosuppressive chemotherapy within 3 weeks prior to study entry (6 weeks if prior nitrosurea,). * Stem Cell Transplant or Rescue: No evidence of active graft vs. host disease and greater than or equal to 2 months must have elapsed. * Steroids: Dose should be stable or decreasing for at least one week prior to starting therapy. Corticosteroid therapy is permissible only for the treatment of increased intracranial pressure in patients with malignancies in the CNS or for spinal cord compression. Corticosteroid should be used at the lowest dose to control symptoms and discontinued if possible. * Must not be receiving tacrolimus or cyclosporine * Biologic (anti-neoplastic) agent: At least 7 days since the completion of therapy with a biologic agent. * XRT: Must not have received XRT within 3 months prior to study entry for craniospinal irradiation (\>24 Gy) or total body irradiation or if greater than or equal to 50% radiation of pelvis; \> 8 weeks for local irradiation to primary tumor; \> 2 weeks for focal irradiation for symptomatic metastatic sites. * Growth factors: Must be off growth factor(s) \> 1 week prior to study entry (GCSF, GM CSF, erythropoietin). * Age: ≤ 21 years. * Organ Function: Must have adequate organ function and marrow function as defined by the following parameters: * Bone marrow: peripheral ANC \> 1,000/µl, hemoglobin \> 8 g/dl (may be transfusion dependent), platelets \> 100,000/µ (transfusion independent). (Patients with bone marrow involvement are eligible provided they meet these criteria). * Hepatic: Bilirubin \< 1.5 x institutional upper limit of normal (IULN), SGPT \< 3 x IULN. * Renal: Normal creatinine for age or GFR \> 70/ml/min/1.73m2. * Cardiac: Must have normal EKG and Echocardiogram with shortening fraction \> 27% or ejection fraction \> 50%. * Pulmonary: No evidence of dyspnea at rest, no exercise intolerance, and a pulse oximetry \> 94% in room air, if there is clinical indication for determination * Central Nervous System: Patients without seizure disorder OR patients with well-controlled seizure disorder receiving anticonvulsants may be enrolled on this protocol. Anticonvulsants must not be enzyme-inducing (i.e., no barbiturates, phenytoin, carbamazepine, etc, please see Appendix II for a list of drugs that are inducers and inhibitors of CYP3A) * Informed consent explained to and signed by parent/legal guardian or patient if the patient is ≥ 18 years. * Patient must begin therapy within 7 calendar days of registration. * Patient must be able to swallow whole tablets Exclusion Criteria: * Concurrently receiving any other concomitant anticancer or experimental drug therapy. * Have ≥ Grade 2 uncontrolled hypertension * History of a stroke, myocardial infarction, or unstable angina in the previous 6 months * Evidence of a bleeding diathesis or PT INR\>1.5 * Pre-existing Coagulopathy * Major surgical procedure(s) within previous 4 weeks prior to study enrollment * Minor surgical procedures within 7 days prior to study enrollment * History of an abdominal fistula, GI perforation, or intra-abdominal abscess within previous 6 months. * A serious, non-healing wound, ulcer, or bone fracture * In patients with CNS tumors or known CNS metastases, evidence of intracranial or intratumoral hemorrhage on baseline MRI obtained within 14 days prior to study registration. * If there is proteinuria present on dipstick, patients are excluded if they have \>500 mg protein on 24 hour urine collection. * Require treatment with any of the medications listed in Appendix II (Excluding dexamethasone: Corticosteroid therapy is permissible only for the treatment of increased intracranial pressure in patients with malignancies in the CNS or for spinal cord compression. Corticosteroid should be used at the lowest dose to control symptoms and discontinued if possible). Use of H2 antagonists such as ranitidine, cimetidine and proton pump blockers such as omeprazole are permissible only in conjunction with corticosteroids in the setting of increased intracranial pressure or for spinal cord compression, as these drugs interfere with CYP3A4. If patients are given such drugs, they must be taken at least 4 hours after intake of everolimus. * Have an uncontrolled infection. * History of infection with the hepatitis B and/or C viruses or positive hepatitis B virus surface antigen and hepatitis C virus antibody. * Pregnant. Females of childbearing potential must have negative serum or urine pregnancy test within 7 days prior to study entry. The effects of everolimus on the developing human fetus are unknown. However, bevacizumab is known to be teratogenic and detrimental to fetal development in animal models. In addition, bevacizumab may alter corpus luteum development and endometrial proliferation, thereby having a negative effect on fertility. For these reasons, women of child-bearing 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 should inform her treating physician immediately and will be removed from the study. * Breastfeeding. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with everolimus or bevacizumab, breastfeeding should be discontinued if the mother is treated on this study. * Inability or unwillingness of research participant or legal guardian/representative to give written informed consent.