A Study Using Regorafenib as Second or Third Line Therapy in Metastatic Medullary Thyroid Cancer

Inclusion Criteria: * Subjects must be able to understand and be willing to sign the written informed consent form. A signed informed consent form must be appropriately obtained prior to the conduct of any trial-specific procedure. * Age ≥ 18 years. * Life expectancy of at least 12 weeks (3 months). * Eastern Cooperative Oncology Group performance status of ≤1. * Histologically or cytologically confirmed diagnosis of metastatic medullary thyroid cancer. * Documented disease progression within 6 months prior to study registration, as defined by RECIST criteria. * Must have at least 1 site of measurable disease by RECIST criteria, by version 1.1. * Archival tissue block or unstained slides (from primary or metastatic site) must be available, otherwise fresh tissue biopsy sample will be collected. * Any number of prior chemotherapies and targeted therapies are allowed. * Patients must have received at least one prior line of targeted therapy. * Adequate bone marrow, liver and renal function as assessed by the following laboratory requirements within 3 weeks prior to study registration: * Total bilirubin ≤ 1.5 x the upper limits of normal (ULN) * Alanine aminotransferase (ALT) and aspartate amino-transferease (AST) ≤ 2.5 x ULN (≤ 5 x ULN for subjects with liver involvement of their cancer) * Alkaline phosphastase limit ≤ 2.5 x ULN (≤ 5 x ULN for subjects with liver involvement of their cancer) * Serum creatinine ≤ 1.5 x the ULN * International normalized ratio (INR)/ Partial thromboplastin time (PTT) ≤ 1.5 x ULN. (Subjects who are prophylactically treated with an agent such as warfarin or heparin will be allowed to participate provided that no prior evidence of underlying abnormality in coagulation parameters exists. Close monitoring of at least weekly evaluations will be performed until INR/PTT is stable based on a measurement that is pre-dose as defined by the local standard of care. (See Section 3.3) * Platelet count \> 100000 /mm3, hemoglobin (Hb) \> 9 g/dL, absolute neutrophil count (ANC) 1500/mm3. Blood transfusion to meet the inclusion criteria will not be allowed. * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to study registration. Post-menopausal women (defined as no menses for at least 1 year) and surgically sterilized women are not required to undergo a pregnancy test. The definition of adequate contraception will be based on the judgment of the investigator. * Subjects (men and women) of childbearing potential must agree to use adequate contraception beginning at the signing of the ICF until at least 2 months after the last dose of study drug. The definition of adequate contraception will be based on the judgment of the principal investigator or a designated associate. * Subject must be able to swallow and retain oral medication. Exclusion Criteria: * Prior treatment with regorafenib. * Previous assignment to treatment during this study. Subjects permanently withdrawn from study participation will not be allowed to re-enter 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. * 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 or coagulopathy. * Any hemorrhage or bleeding event ≥ NCI CTCAE Grade 3 within 4 weeks prior to start of study medication. * 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. * Subjects with any previously untreated or concurrent cancer that is distinct in primary site or histology except cervical cancer in-situ, treated basal cell carcinoma, or superficial bladder tumor. Subjects surviving a cancer that was curatively treated and without evidence of disease for more than 3 years before registration 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). * Patients with pheochromocytoma. * 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 v4.0. * Symptomatic metastatic brain or meningeal tumors. * Presence of a non-healing wound, or non-healing ulcer, (that is not tumor related) or bone fracture. * Major surgical procedure or significant traumatic injury within 28 days before start of study medication. * Other investigational treatment during or within 30 days before starting study treatment. * Use of any approved tyrosine kinase inhibitors within 2 weeks or 6 half-lives of the agen, whichever is shorter, prior to receiving study drug. * Prior radiation within 14 days before start of study medication.Renal failure requiring hemo-or peritoneal dialysis. * Dehydration Grade ≥1 NCI-CTCAE v4.0. * Patients with seizure disorder requiring medication. * Persistent proteinuria ≥ Grade 3 NCI-CTCAE v4.0 (\> 3.5 g/24 hrs, measured by urine protein: creatinine ratio on a random urine sample). * 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 4.0 Grade 2 dyspnea). * 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. * 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. * Excluded therapies and medications, previous and concomitant * Concurrent anti-cancer therapy (chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, or tumor embolization) other than study treatment (regorafenib, other agents being investigated in combination with regorafenib). * Prior use of regorafenib. * Concurrent use of another investigational drug or device therapy (i.e., outside of study treatment) during, or within 4 weeks of trial entry (signing of the informed consent form). * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days before start of study medication. * Therapeutic anticoagulation with Vitamin-K antagonists (e.g., warfarin) or with heparins and heparinoids. \--- However, prophylactic anticoagulation as described below is allowed: * Low dose warfarin (1 mg orally, once daily) with PT-INR ≤ 1.5 x ULN is permitted. Infrequent bleeding or elevations in PT-INR have been reported in some subjects taking warfarin while on regorafenib therapy. Therefore, subjects taking concomitant warfarin should be monitored regularly for changes in PT, PT-INR or clinical bleeding episodes. * Low dose aspirin (≤ 100 mg daily). * Prophylactic doses of heparin. * Use of any herbal remedy (e.g. St. John's Wort \[Hypericum perforatum\])