Inclusion Criteria:

• Age ≥ 10 years for Liposarcoma, Osteosarcoma, and Ewing sarcoma; Age ≥ 5 years for Rhabdomyosarcoma cohorts
• Weight ≥ 15 kg (33 lb)
• Patients must have histologically or cytologically confirmed advanced/metastatic liposarcoma, osteogenic sarcoma, Ewing/Ewing-like sarcoma of soft tissue or bone, fusion-positive alveolar rhabdomyosarcoma or embryonal rhabdomyosarcoma/fusion-negative alveolar rhabdomyosarcoma
• WHO Performance Status 0, 1 or 2. A maximum of 1/3 of patients in cohorts A & B may be WHO performance status 2
• At least one prior line of systemic therapy for the sarcoma diagnosis (neoadjuvant, adjuvant or metastatic disease)
• All acute toxic effects of any prior treatment have resolved to NCI-CTCAE v 4.0 Grade 1 or less (except alopecia) at the time of signing the Informed Consent Form (ICF)
• Subject must be able to swallow and retain oral medication
• At least one site of measurable disease on x-ray/CT/MRI scan as defined by RECIST 1.1
• Adequate organ function within 14 days of registration
• Evidence of progression of disease as defined by RECIST 1.1 (i.e. new disease sites or 20% growth of index lesions) within 6 months of registration
• Patients with central nervous system disease are eligible for enrollment if they have received prior radiotherapy or surgery to sites of CNS (central nervous system) metastatic disease and are without evidence of clinical progression for at least 12 weeks after therapy

Exclusion Criteria:

• Patients with documentation of well differentiated liposarcoma only (of the well differentiated/dedifferentiated liposarcoma family) are specifically excluded, owing to its characteristically slow growth. If high grade areas are suspected (dedifferentiation), but not proved by pathology analysis (e.g. after primary resection of a well-differentiated liposarcoma), a biopsy must be performed to demonstrate the high-grade dedifferentiated disease
• Prior systemic therapy with a small molecule oral kinase inhibitor, including but not limited to: pazopanib, sunitinib, sorafenib, everolimus, sirolimus, vemurafenib, dasatinib and trametinib
• Previous assignment to treatment during this study. Subjects permanently withdrawn from study participation will not be allowed to re-enter study. Patients who progress on placebo are specifically allowed to enroll on the treatment arm of the study if they meet all other entry criteria
• Concurrent, clinically significant, active malignancies within 12 months of study enrollment
• Patients with severe and/or uncontrolled concurrent medical disease that in the opinion of the investigator could cause unacceptable safety risks or compromise compliance with the protocol
• Major surgery within 28 days prior to study registration or those patients who have not recovered adequately from prior surgery
• Patients who have received wide field radiotherapy ≤ 28 days (defined as > 50% of volume of pelvis bones or equivalent) or limited field radiation for palliation < 14 days prior to study registration or those patients who have not recovered adequately from side effects of such therapy
• Patients who have received prior systemic therapy < 14 days prior to study registration or have not recovered adequately from toxicities to CTCAE v. 4.03 grade 1 or less; prior investigational therapy may not have been given < 5 half-lives of last dose of treatment, or < 14 days, whichever is greater
• Uncontrolled hypertension (systolic pressure >140 mm Hg or diastolic pressure > 90 mm Hg [NCI-CTCAE v 4.0] on repeated measurement) despite optimal medical management
• Active or clinically significant cardiac disease including: Congestive heart failure-New York Heart Association (NYHA) > class II, Active coronary artery disease, Cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin, Unstable angina (anginal symptoms at rest), new onset angina within 3 months before randomization, or myocardial infarction within 6 months before randomization
• Evidence or history of bleeding diathesis
• Any hemorrhage or bleeding event ≥ NCI CTCAE Grade 3 within 4 weeks prior to study registration
• Subjects with thrombotic, embolic, venous, or arterial events, such as cerebrovascular accident (including transient ischemic attacks) deep vein thrombosis or pulmonary embolism within 6 months of start of study treatment
• Known history of human immunodeficiency virus (HIV) infection or current chronic or active hepatitis B or C infection requiring treatment with antiviral therapy.
• Ongoing infection > Grade 2 NCI-CTCAE v 4.03
• Presence of a non-healing wound, non-healing ulcer, or benign bone fracture (patients with stress insufficiency fractures e.g. from osteoporosis or pathological fracture from tumor are eligible for study)
• Patients with seizure disorder requiring medication
• Proteinuria > 100 mg/dl on urine analysis
• Interstitial lung disease with ongoing signs and symptoms at the time of informed consent
• Pleural effusion or ascites that causes respiratory compromise (≥ NCI-CTCAE version 4.03 Grade 2 dyspnea)
• History of organ allograft (including corneal transplant).
• Known or suspected allergy or hypersensitivity to regorafenib, or excipients of the formulations given during the course of this trial
• Any malabsorption condition.
• Women who are pregnant or breast-feeding.
• Any condition which, in the investigator's opinion, makes the subject unsuitable for trial participation
• Substance abuse, medical, psychological or social conditions that may interfere with the subject's participation in the study or evaluation of the study results
• Inability to comply with protocol required procedures
• Use of any herbal remedy (e.g. St. John wort [Hypericum perforatum])