A subject must meet all of the following inclusion criteria to be included in the study: 1. Provide written informed consent (Subject or legal representative) 2. Be > 6 months and < 18 years of age. For each dose cohort in Part A, the first 3 subjects must be at least 2 years of age. 3. Have a histologically-confirmed diagnosis of MB, NB, ES, or ARMS 4. Have documented relapse or refractoriness after standard-of-care therapy 5. Have undergone magnetic resonance imaging (MRI) for MB, a computerized tomography (CT) / metaiodobenzylguanidine (MIBG) scan (if MIBG avid) for NB, CT / MRI for ES or ARMS within 1 month prior to first dose of study treatment 6. Have a Lansky score >= 40 for subjects up to 16 years of age or a Karnofsky score >= 40 for subjects 16 years of age to < 18 years 7. Have adequate organ function, defined as: * Peripheral absolute neutrophil count >= 1.5 x 109/L * Platelet count >= 100 x 109/L (transfusion to reach this level is permitted) * Hemoglobin >= 8mg/dL (transfusion to reach this level is permitted) * International normalized ratio (INR) < 1.5; partial thromboplastin time (PTT) < 1.5 upper limit of normal (ULN) * Creatinine clearance > 50 mL/min/1.73m2 OR serum creatinine <= specified maximum values based on age as described below: * 6 months to 3 years of age: serum creatinine <= 0.4mg/dL * 3 to 13 years of age: serum creatinine <= 0.7mg/dL * > 13 years of age: serum creatinine <= 1mg/dL * Serum aspartate aminotransferase (AST) and serum alanine aminotransferase (ALT) < 2.5 x ULN; serum total bilirubin < 1.5 x ULN 8. Have no symptoms of cranial hypertension or convulsions within 14 days before Cycle 1 Day 1 (anti-epileptic drugs and corticoids are allowed to control any preexisting symptoms) 9. If female of child bearing potential, must not be lactating and must have a negative pregnancy test (blood or urine, at the discretion of the investigator) prior to enrollment and use effective contraception during study participation. Women should continue effective contraception for 3 months following last dose of TB-403. 10. If a sexually-active male, must agree to use a latex condom during any sexual contact with females of child bearing potential while participating in the study and for 3 months following last dose of TB-403. 11. For subjects on corticosteroids for endocrine deficiencies or tumor-associated symptoms, must be on a stable (or decreasing) dose for at least 7 days before first dose of study treatment. Additional Criteria for Sub-Studies: Subjects who are willing to participate in the CSF sub-study must sign additional informed consent. Subjects who are willing to participate in the correlative biologic sub-study must sign additional informed consent to provide tumor tissue for analysis of protein and gene expression.