Ponatinib for Advanced Medullary Thyroid Cancer

Background: * Medullary thyroid cancer (MTC) represents 5% of thyroid cancers and presents as a hereditary (25% of cases) or sporadic (75% of cases) neuroendocrine malignancy. * MTC arises from the parafollicular C-cells of the thyroid. * Germline mutations in the rearranged during transfection (RET) proto-oncogene occur in virtually all of hereditary MTC cases, and somatic RET mutations occur in 50% of sporadic cases. * Drugs targeting RET kinase such as vandetanib and cabozantinib have shown efficacy in the treatment of advanced or metastatic MTC, however, more effective RET inhibitors are needed for previously untreated patients as well as patients who have become refractory to other molecular targeted therapeutics (MTTs). * Ponatinib, a drug that is Food and Drug Administration (FDA) approved as a therapy for chronic myelogenous leukemia (CML) and Philadelphia chromosome-positive acute lymphoblastic leukemia (Ph+ ALL), is a potent inhibitor of RET kinase. Primary Objective: -To determine the objective overall response rate (complete response \[CR\] + partial response \[PR\] by Response Evaluation Criteria in Solid Tumors (RECIST) to ponatinib in the treatment of patients with advanced or metastatic MTC previously treated with cabozantinib and vandetanib who: 1) have tumors with RET mutations and 2) have tumors without RET mutations. Eligibility: * Patients must have histologically confirmed, unresectable, locally advanced or metastatic MTC, with measurable disease by RECIST criteria. * Patients must have disease amenable to biopsy and be willing to undergo biopsy for molecular analysis, and also have adequate archival material from their thyroidectomy or from a tumor biopsy obtained prior to beginning any systemic therapy. * Patients must have failed or been intolerant to prior treatment with both cabozantinib and vandetanib. * The last dose of prior systemic therapy must be more than 28 days prior to the first dose of ponatinib * Radiation therapy is per