Ponatinib in Advanced or Metastatic Medullary Thyroid Cancer

Inclusion Criteria: * Diagnosis of localized or metastatic unresectable MTC. * Measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥20 mm with conventional techniques or as ≥10 mm with spiral computerized tomography (CT) scan. * The last dose of previous therapy targeting RET kinase must be given at least 4 weeks - Previous treatment with cytotoxic chemotherapy, immunotherapy, or radiotherapy are permitted, if the last dose was given at least 4 weeks prior to the first dose of ponatinib * Patient must have failed (progressed on or been intolerant of) prior treatment with cabozantinib or vandetanib. * Age ≥18 years old * Eastern Cooperative Oncology Group (ECOG) performance status ≤2 * Normal organ and marrow function as defined below: * Negative pregnancy test for women of childbearing potential or male patients, even if surgically sterilized (i.e., status post-vasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug, or * Agree to completely abstain from heterosexual intercourse * Normal QT interval corrected on screening electrocardiogram (ECG) evaluation, defined as the corrected QT interval by Fredericia (QTcF) of ≤450 ms. * Ability to understand and the willingness to sign a written informed consent document and follow the guidelines of the clinical protocol including visits for treatment and follow up * Life expectancy of greater than 12 weeks * Available archival tissue or willingness to undergo fresh biopsy if no archival tissue is available. Exclusion Criteria: * Patients who are receiving any other investigational agent. * Patients with brain metastases or spinal cord compression unless they completed radiation therapy ≥4 weeks prior to the first dose of ponatinib and are stable without steroids or anti-convulsant therapy for ≥10 days. * Patients who cannot discontinue medications that are known to be associated with Torsades de Pointes. These medications are listed in Attachment 3 * Uncontrolled hypertension (systolic blood pressure \>150 or diastolic blood pressure \>100 * Significant or active cardiovascular disease within 6 months prior to enrollment * A history of pancreatitis or alcohol abuse * Uncontrolled hypertriglyceridemia (\>450 mg/dL) * Major surgery (with the exception of minor surgical procedures, such as catheter placement or tumor biopsy) within 28 days prior to the first dose of ponatinib * Ongoing or active infection including known history of human immunodeficiency virus (HIV), hepatitis B virus (HBV), or hepatitis C (HCV). Testing for these viruses is not required in the absence of a history of infection. * Suffer from any condition or illness that, in the opinion of the investigator, would compromise patient safety or interfere with the evaluation of the safety of the study drug * Evidence of a bleeding diathesis that cannot be corrected with standard therapy or factor replacement * Presence of another primary malignancy within the past 2 years (except for non-melanoma skin cancer or cervical cancer in situ. Prior prostate cancer is also permitted if prostate-specific antigen (PSA) is now undetectable) * Pregnant or lactating * History of allergic reactions attributed to compounds of similar chemical or biologic composition to investigational agent