The research study procedures include screening for eligibility and study treatment including evaluations and follow up visits.

* This research study involves the study drug selpercatinib in combination with standard of care treatments, I-131 and thyrotropin alfa (rhTSH). Participants receive study treatment for as long as the disease does not worsen (disease progression) for approximately 1 month for up to two courses of treatment, if participants do not experience any unacceptable side effects, and/or until withdrawal of consent. * Participants will be followed for 2 years from the date of study registration. * It is expected that about 30 people will take part in this research study/ * This research study is a Phase II clinical trial. Phase II clinical trials test the safety and effectiveness of an investigational drug to learn whether the drug works in treating a specific disease. "Investigational" means that the drug is being studied.

* The U.S. FDA has approved selpercatinib, I-131 and rhTSH as a treatment option for this disease. * The combination therapy is investigational as it has not been approved to treat this disease. * Selpercatinib, I-131 and rhTSH are standard of care treatment options for thyroid cancer. Selpercatinib is a small molecule designed to block the active RET signaling.