This research study is a Phase II clinical trial, which tests the safety and effectiveness of an investigational drug to learn whether the drug works in treating a specific cancer. "Investigational" means that the drug is being studied.

It has been found that some people with NSCLC have a change (mutation) in a certain gene called the RET gene. This mutated gene may help cancer cells grow. Only participants with a RET mutation will be allowed to participate. In this study, investigators are testing the strategy of using a study drug designed to inhibit or shut off growth signals that results from the mutated RET gene.

Ponatinib is an anti-cancer drug that has been used in research studies for other types of cancer. Ponatinib blocks several growth signals in cancer cells, including RET. In this research study, investigators are looking to see whether ponatinib is effective and safe in treating NSCLC harboring RET rearrangements.

Participants in this research study will be asked to undergo some screening tests or procedures to confirm that eligibility. Many of these tests and procedures are likely to be part of regular cancer care and may be done even if it turns out that participants do not take part in the research study. These tests and procedures include the following: medical history, vital signs, physical exam, performance status, electrocardiogram, echocardiogram, routine blood tests, pregnancy test and an assessment of tumor by CT or MRI. If these tests show that a participant is eligible to participate in the research study, he/she will begin the study treatment. If a patient does not meet the eligibility criteria, he/she will not be able to participate in this research study.

Participants will take the study drug once a day, every day of the cycle. Each treatment cycle lasts 28 days (4 weeks). Participants will be given a drug diary to record the drug they take each day. The diary will also include special instructions for taking the study drug.

For cycles 1-20, participants will visit the clinic to have tests and procedures done at the time points listed here: On Day 1-physical exam, vital signs, performance status, electrocardiogram, routine blood tests, pharmacokinetic test, clinical exam and assessment of tumor. On day 15 of cycle 1-vital signs, routine blood tests and clinical exam.

For cycles 11 and on, participants will visit the clinic every 6 weeks. Some of these visits will happen on Day 1 of the cycle and some of these visits will happen on Day 15 of the cycle. At each visit, the following tests and procedures will be done: physical exam, vital signs, performance status, electrocardiogram, routine blood tests, clinical exam, and an assessment of your tumor.

Participants will visit the clinic when their study doctor takes them off study drug permanently. They will also visit the clinic 30 days after stop taking the study drug. The following tests and procedures will be done: physical exam, vital signs, performance status, electrocardiogram, routine blood tests, pregnancy test, clinical exam and a tumor assessment.

Investigators would also like to keep track of participant's medical condition for two years after their first study dose. Investigators will contact participants by telephone every 3 months. If participants still come to the clinic, visits might be used as contact.

Inclusion Criteria:

• Histologically or cytologically confirmed advanced NSCLC
• Molecular confirmation of a RET translocation
• At least one measurable lesion as defined by RECIST
• No restriction on number of prior therapies
• Estimated life expectancy of at least 12 weeks
• Able to swallow and retain orally administered medication
• Must agree to use an effective form of contraception from enrollment through 30 days after the end of study treatment
• Willingness and ability to comply with scheduled visits and study procedures

Exclusion Criteria:

• Clinically significant gastrointestinal abnormalities
• Pregnant or breastfeeding
• Major surgery within 28 days of initiating therapy
• History of CNS disease (Note: Participants with brain metastases will be eligible if treated appropriately and if they remain clinically stable).
• Anti-cancer therapy within 3 weeks
• History of significant bleeding disorder unrelated to cancer
• History of acute pancreatitis within 1 year of study entry or history of chronic pancreatitis
• History of alcohol abuse
• Uncontrolled hypertriglyceridemia
• History of arterial thrombotic events (myocardial infarction, stroke or peripheral vascular disease).
• Uncontrolled hypertension
• Taking medications that are known to be associated with Torsades de Pointes
• Ongoing active infection
• Diagnosed with or received anti-cancer therapy for another primary malignancy within 3 years prior to entry (except for non-melanoma skin cancer or in situ cancers)
• Any condition or illness tha could compromise patient safety or interfere with the evaluation of the drug

From the start of treatment until 30 days after the end of treatment (up to approximately 2 years)