Sorafenib and Topotecan in Refractory/Recurrent Pediatric Malignancies

Inclusion Criteria: * Life expectancy of at least 12 weeks (3 months) * Must have had relapsed or refractory solid tumor malignancy, or a relapsed or refractory central nervous system malignancy AND must have received at least one prior course of therapy for their malignancy. * Patients with a solid tumor must have radiographic evidence of disease. Bone only disease is acceptable if biopsy proven but will not be eligible for response criteria by RECIST 1.1. Ideally patients will have disease evaluable by RECIST 1.1. * Patient's 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 ≥ 50 for patients \> 16 years of age, and Lansky ≥ 50 for patients ≤ 16 years of age. * Prior Therapy: Patients with solid tumors must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study. 1. Previous Sorafenib or Topotecan: Patients may not have previously been treated with sorafenib. Patients may have been previously treated with topotecan provided it was in combination with other agents and the most recent dose was more than 6 months from study entry. Patients in whom disease has progressed on single agent topotecan will not be eligible for this study. 2. Myelosuppressive Chemotherapy: Patients with solid tumors must not have received myelosuppressive chemotherapy within 3 weeks or nitrosourea within 6 weeks of entry onto this study. 3. Hematopoietic Growth Factors: At least 7 days since the completion of therapy with a growth factor and at least 14 days since pegfilgrastim (Neulasta®) administration. 4. Biologic (anti-neoplastic agent): At least 21 days or 5 half lives (whichever is greater duration) since the completion of therapy with 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. 5. Radiation Therapy (XRT): ≥ 4 wks for local palliative XRT (small port); ≥ 3 months must have elapsed if prior TBI, or craniospinal XRT or if ≥ 50% radiation of pelvis; ≥ 6 weeks must have elapsed if other substantial bone marrow (BM) radiation. 6. Stem Cell Transplant or Rescue without total body irradiation (TBI): For allograft: no evidence of active graft vs. host disease and ≥ 3 months must have elapsed since stem cell transplantation (SCT). Autologous transplant recipients must be transfusion independent and not require growth factors for \>4 weeks. * All patients and/or their parents or legal guardians must sign a written informed consent. Assent, when appropriate will be obtained according to local Institutional Review Board (IRB) guidelines. A signed informed consent form must be appropriately obtained prior to the conduct of any trial-specific procedure. * Organ Function Requirements - Adequate Bone Marrow Function Defined As: 1. Peripheral absolute neutrophil count (ANC) ≥ 1500/μL. 2. Platelet count ≥ 100,000/μL (transfusion independent, defined as not receiving platelet transfusions within a 7 day period prior to enrollment) 3. Hemoglobin ≥ 10.0 gm/dL (may receive red blood cell transfusions) 4. Patients with known bone marrow metastatic disease will be eligible for study. These patients must not be known to be refractory to red cell or platelet transfusion. If dose limiting hematologic toxicity is observed, all subsequent patients enrolled at the dose level must not have bone marrow metastatic disease. * Adequate Renal Function Defined As: Creatinine clearance or radioisotope glomerular filtration rate (GFR) ≥ 60ml/min/1.73 m\^2, or serum creatinine based on age/gender as defined in the Schwartz formula for estimating GFR (Schwartz et al. J. Peds, 106:522, 1985) utilizing child length and stature data published by the Centers for Disease Control and Prevention (CDC). * Adequate Liver Function Defined As: 1. Bilirubin (sum of conjugated + unconjugated) ≤ upper limit of normal (ULN) for age 2. Alanine transaminase (ALT) ≤ upper limit of normal for age 3. All clinically significant chemistries excluding alkaline phosphatase, uric acid, aspartic transaminase (AST) and lactate dehydrogenase (LDH) must be grade 1 or less * Adequate Cardiac Function Defined As: 1. Normal 12 lead EKG with corrected QT interval (QTc) \< 450 msec, and either: 2. Shortening fraction ≥ 28% or left ventricular ejection fraction ≥ 50%. 3. Systolic Blood Pressure and Diastolic Blood Pressure ≤ 95th percentile for age and gender * Adequate Pulmonary Function Defined As: No evidence of dyspnea at rest, and a resting pulse oximetry \> 92%. * All acute toxic effects of any prior treatment have resolved to NCI-CTCAE v4.0 Grade 1 or less at the time of enrollment, signing the Informed Consent Form (ICF). * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment. * Prothrombin time-international normalized ratio (PT-INR) ≤ 1.5 X ULN and partial thromboplastin time (PTT) or activated partial thromboplastin time (aPTT) ≤ 1.5 X ULN. * Participants (men and women) of childbearing potential must agree to use adequate contraception beginning at the signing of the ICF until at least 30 days after the last dose of study drug. * Must be able to swallow and retain oral medication Exclusion Criteria: * Previous assignment to treatment during this study * Uncontrolled hypertension (systolic pressure \>140 mm Hg or diastolic pressure \> 90 mm Hg \[NCI-CTCAE v4.0\] on repeated measurement) despite optimal medical management * Evidence or history of bleeding diathesis or coagulopathy * Any pulmonary hemorrhage/bleeding event of NCI-CTCAE v4.0 Grade 2 or higher within 4 weeks of treatment; any other hemorrhage/bleeding event of NCI-CTCAE v4.0 Grade 3 or higher within 4 weeks of treatment * Have used strong cytochrome P450 3A4 (CYP3A4) inducers (eg, phenytoin, carbamazepine, phenobarbital, St. John's Wort \[Hypericum perforatum\], dexamethasone at a dose of greater than 16 mg daily, or rifampin \[rifampicin\], and/or rifabutin) within 28 days before treatment * Any previously untreated or concurrent cancer that is distinct in primary site or histology from the primary. Patients surviving a cancer that was curatively treated and without evidence of disease for more than 3 years before randomization are allowed. All cancer treatments must be completed at least 3 years prior to study entry (i.e., signature date of the informed consent form) * Presence of a non-healing wound, non-healing ulcer, or bone fracture * History of organ allograft. (Including corneal transplant) * Known or suspected allergy or hypersensitivity to any of the study drugs, study drug classes, or excipients of the formulations given during the course of this trial * Women who are pregnant or breast-feeding * Inability to comply with the protocol and/or not willing or not available for follow-up assessments * Any condition which, in the investigator's opinion, makes the patient unsuitable for trial participation