ADVL1711, A Phase 1/2 Study of Lenvatinib in Combination With Everolimus in Recurrent and Refractory Pediatric Solid Tumors, Including CNS Tumors

1. Histologically or cytologically confirmed diagnosis of the following tumor types: a. Phase 1: Recurrent or refractory solid tumors (excluding hepatoblastoma and lymphomas), including primary central nervous system (CNS) tumors; subjects must have either measurable or evaluable disease. b. Phase 2: Recurrent or refractory tumors; subjects must have measurable disease * Cohort 1: Ewing sarcoma/peripheral primitive neuroectodermal tumor (pPNET) * Cohort 2: Rhabdomyosarcoma * Cohort 3: High grade glioma (HGG) (subjects with Diffuse Intrinsic Pontine Glioma are not eligible) 2. Measurable disease that meets the following criteria (Phase 2): a. Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 (for all tumor types except HGG) * At least 1 lesion of >= 1.0 cm in the longest diameter for a non lymph node or >= 1.5 cm in the short-axis diameter for a lymph node which is serially measurable according to RECIST 1.1 using computed tomography/magnetic resonance imaging (CT/MRI). If there is only one target lesion and it is a non-lymph node, it should have a longest diameter of >= 1.5 cm. b. Response Assessment in Neuro-Oncology (RANO) for high grade glioma (HGG) * At least one lesion must be measurable as defined as a bi-dimensionally contrast-enhancing lesion with clearly defined margins by CT or MRI scan, with a minimal diameter of 1 cm, and visible on 2 axial slices which are preferably at most 5 mm apart with 0 mm skip. Lesions that have had external beam radiotherapy (EBRT) or locoregional therapies such as radiofrequency (RF) ablation must show evidence of progressive disease based on RECIST 1.1 to be deemed a target lesion. 3. Karnofsky performance score >= 50 for subjects > 16 years of age and Lansky play score >= 50 for subjects <= 16 years of age. Note: Neurologic deficits in subjects with CNS tumors must have been relatively stable for at least 7 days prior to study enrollment. Subjects 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. 4. Subjects must have fully recovered from the acute toxic effects of all prior anti-cancer therapy and must meet the following minimum duration from prior anti-cancer directed therapy prior to enrollment. If after the required timeframe, the numerical eligibility criteria are met, eg, blood count criteria, the subject is considered to have recovered adequately. a. Cytotoxic chemotherapy or other chemotherapy known to be myelosuppressive: >= 21 days after the last dose of cytotoxic or myelosuppressive chemotherapy (42 days if prior nitrosourea). b. Anti-cancer agents not known to be myelosuppressive (eg, not associated with reduced platelet or absolute neutrophil counts): >= 7 days after the last dose of agent. c. Monoclonal antibodies: >= 21 days or 3 half-lives (whichever is shorter) of the antibody must have elapsed after the last dose of a monoclonal antibody (including immune checkpoint inhibitors). Toxicity related to prior antibody therapy must be recovered to Grade <= 1. d. Corticosteroids: If used to modify immune adverse events (AEs) related to prior therapy, >= 14 days must have elapsed since last dose of corticosteroid. Subjects 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. e. Hematopoietic growth factors: >= 14 days after the last dose of a long-acting growth factor (eg, Neulasta) or 7 days for short-acting growth factor. For agents that have known AEs occurring beyond 7 days after administration, this period must be extended beyond the time during which AEs are known to occur. f. Interleukins, interferons, and cytokines (other than hematopoietic growth factors): >= 21 days after the completion of interleukins, interferons or cytokines (other than hematopoietic growth factors). g. Stem cell infusions (with or without total body irradiation [TBI]): * Allogeneic (non-autologous) bone marrow or stem cell transplant, or any stem cell infusion including donor leukocytes infusion or boost infusion: >= 84 days after infusion and no evidence of graft versus host disease (GVHD). * Autologous stem cell infusion including boost infusion: >= 42 days h. Cellular Therapy: >= 42 days after the completion of any type of cellular therapy (eg, modified T cells, natural killer cells, dendritic cells, etc). i. Radiotherapy (XRT)/External Beam Irradiation including Protons: >= 14 days after local XRT; >= 150 days after total body irradiation, craniospinal XRT or if radiation to >= 50% of the pelvis; >= 42 days if other substantial bone marrow radiation. j. Radiopharmaceutical therapy (eg, radiolabeled antibody, iodine-131 metaiodobenzylguanidine [131I-MIBG]): >= 42 days after systemically administered radiopharmaceutical therapy. k. VEGF/VEGFR (vascular endothelial growth factor (receptor))-targeted or mTOR (mammalian target of rapamycin)-targeted therapies: * Must not have received prior exposure to lenvatinib * May have previously progressed on an mTOR inhibitor * No more than 2 prior VEGF/VEGFR-targeted therapies (For Phase 2 only) * Must not have received prior VEGF/VEGFR-targeted therapy in combination with an mTOR inhibitor (For Phase 2 only) 5. Male or female subjects must be >= 2 years and <= 21 years of age 6. Adequate bone marrow function: * For subjects with solid tumors without known bone marrow involvement: o Peripheral absolute neutrophil count (ANC) >= 1000/mm3 o Platelet count >= 100,000/mm3 o Hemoglobin >= 8.0 g/dL at baseline (may receive red blood cell transfusions) * For subjects with known bone marrow metastatic disease: o Peripheral ANC >= 1000/mm3 o Platelet count >= 100,000/mm3 (and with no platelet transfusions for at least 7 days prior to enrollment) o May receive transfusions provided they are not known to be refractory to red cell or platelet transfusions. These subjects will not be evaluable for hematologic toxicity. At least 5 of every cohort of 6 subjects with a solid tumor must be evaluable for hematologic toxicity, for the dose-escalation part of the study. If dose-limiting hematologic toxicity is observed, all subsequent subjects enrolled must be evaluable for hematologic toxicity. 7. Adequate renal function: * Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70 mL/min/1.73 m2 or * A serum creatinine based on age/gender as listed in the protocol. * Urine dipstick < 2+ for proteinuria. Subjects who have >= 2+ proteinuria on dipstick urinalysis should undergo a spot protein-creatinine (P/C) ratio that should be Grade < 2 per Common Terminology Criteria for Adverse Events (CTCAE) v4.03, and if possible, perform a 24-hour urine collection (children and adolescents <= 12 years of age must have <= 500 mg of protein/24 hours and subjects > 12 years of age must have <= 1 g of protein/24 hours). 8. Adequate liver function: * Bilirubin (sum of conjugated + unconjugated) <= 1.5 x upper limit of normal (ULN) for age, except for unconjugated hyperbilirubinemia of Gilbert[Single Quote]s syndrome. * ALT (alanine aminotransferase) and AST (aspartate aminotransferase) <=3 x ULN * Serum albumin >= 2 g/dL 9. Adequate cardiac function: * Adequate cardiac function as evidenced by left ventricular shortening fraction of >= 27% by echocardiogram or left ventricular ejection fraction (LVEF) >= 50% at baseline, as determined by echocardiography/multigated acquisition (MUGA) scan. * QT interval corrected for heart rate using Fridericia[Single Quote]s formula (QTcF) <= 480 msec. 10. Adequate neurologic function: * Subjects with seizure disorder may be enrolled if on non-enzyme-inducing anticonvulsants and well controlled. * Nervous system disorders (CTCAE v4.03) resulting from prior therapy and not tumor-induced must be <= Grade 2. 11. Adequate blood pressure (BP) control with or without antihypertensive medications, defined as: A BP < the 95th percentile for sex, age and height/length (<= 150/90 mmHg for subjects aged 18 - 21 years) at Screening (as per National Heart Lung and Blood Institute [NHLBI] guidelines; Appendix 7 and Appendix 8) and no change in antihypertensive medications within 1 week prior to Cycle 1 Day 1. 12. Adequate coagulation: * International Normalized Ratio (INR) <= 1.5 13. Adequate pancreatic function: * Serum amylase <= 1.5 x ULN * Serum lipase <= 1.5 x ULN 14. Adequate metabolic function: * Serum triglycerides <= 300 mg/dL 15. Subjects must have a minimum body surface area (BSA) of 0.6 m2 at study entry, with the exception of Dose Level 2B which requires a minimum BSA of 1.33 m2.