Encorafenib and Binimetinib With or Without Nivolumab in Treating Patients With Metastatic Radioiodine Refractory BRAF V600 Mutant Thyroid Cancer

PRIMARY OBJECTIVES: I. To assess the overall rate of response among study participants treated with the combination of encorafenib and binimetinib, with or without nivolumab. SECONDARY OBJECTIVES: I. To assess the progression-free survival (PFS) among study participants treated with the combination of encorafenib and binimetinib with or without nivolumab. II. To assess the overall survival (OS) among study participants treated with the combination of encorafenib and binimetinib with or without nivolumab. III. To evaluate the duration of response (DOR). IV. To evaluate the safety and tolerability of study participants treated with the combination of encorafenib and binimetinib with or without nivolumab. OUTLINE: Patients are randomized to 1 of 2 arms. ARM I: Patients receive encorafenib orally (PO) once daily (QD) and binimetinib PO twice daily (BID) on days 1-28. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. ARM II: Patients receive encorafenib PO QD and binimetinib PO BID as in arm I. Patients also receive nivolumab intravenously (IV) over 30 minutes on day 1. Cycles with nivolumab repeat every 28 days for up to 2 years in the absence of disease progression or unacceptable toxicity. Please note: Arm II is closed to accrual. Patients will only be enrolled into Arm I as of March 11th, 2022. After completion of study treatment patients are followed up at 30 days and then every 6 months for up to 12 months.