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

Exclusion Criteria

• •Currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational agent/device within 4 weeks of first dose of study intervention
• •* Note: Individuals in the follow-up phase of a prior investigational study may participate as long as it has been 4 weeks since last dose of the previous investigational agent of device
• •Participants with active, known, or suspected autoimmune disease. Participants with type I diabetes mellitus, residual hypothyroidism due to autoimmune thyroiditis only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment are permitted to enroll
• •Prior treatment with selective/potent BRAF/MEK inhibitors including vemurafenib, dabrafenib, encorafenib, selumetinib, trametinib, cobimetinib, binimetinib.
• •* Note: Prior therapy with oral multikinase inhibitors (e.g., lenvatinib, sorafenib, cabozantinib, pazopanib, sunitinib, etc.) remain eligible for study participation.
• •Prior treatment with anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-CTLA-4 antibody (including ipilimumab or any other antibody or drug specifically targeting T cell co-stimulation or immune checkpoint pathways)
• •Participants with a condition requiring systemic treatment with either corticosteroids (\>= 10 mg daily prednisone or equivalent) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids are permitted in the absence of active autoimmune disease
• •History of allergy or hypersensitivity to any monoclonal antibody
• •History or current evidence of retinal vein occlusion (RVO) or current risk factors to RVO (e.g. uncontrolled glaucoma or ocular hypertension, history of hyperviscosity or hypercoagulability syndromes); history of retinal degenerative disease
• •Previous or concurrent malignancy within 3 years of study entry, with the following exceptions:
• •* Adequately treated basal or squamous cell skin cancer, superficial bladder cancer, prostate intraepithelial neoplasm, carcinoma in-situ of the cervix, or other noninvasive or indolent malignancy; OR
• •* Other solid tumors treated curatively in which the expected rate of recurrence within 5 years is \< 5%
• •Impaired cardiovascular function or clinically significant cardiovascular diseases, including any of the following:
• •* History of acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) \< 6 months prior to screening
• •* Symptomatic congestive heart failure (i.e. grade 2 or higher), history or current evidence of clinically significant cardiac arrhythmia and/or conduction abnormality \< 6 months prior to screening. Exceptions include asymptomatic/well-controlled atrial fibrillation/flutter or paroxysmal supraventricular tachycardia
• •* Uncontrolled hypertension defined as persistent elevation of systolic blood pressure \>= 150 mmHg or diastolic blood pressure \>= 100 mmHg, despite medical therapy
• •History of thromboembolic or cerebrovascular events =\< 12 weeks prior to the first dose of study treatment. Examples include transient ischemic attacks, cerebrovascular accidents, hemodynamically significant (i.e., massive or sub-massive) deep vein thrombosis or pulmonary emboli
• •* Note: Individuals with either deep vein thrombosis or pulmonary emboli that does not result in hemodynamic instability are allowed to enroll as long as they are on a stable dose of anticoagulants for at least 4 weeks
• •* Note: Individuals with thromboembolic events related to indwelling catheters or other procedures may be enrolled
• •Known positive serology for HIV (human immunodeficiency virus), active hepatitis B, and/or active hepatitis C infection
• •Known history of acute or chronic pancreatitis
• •Impaired gastrointestinal function or disease that may significantly alter the absorption of encorafenib or binimetinib (e.g., uncontrolled vomiting or malabsorption syndrome)
• •Concurrent neuromuscular disorder that is associated with the potential of elevated creatine kinase (CK) (e.g., inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy)
• •Current use of a prohibited medication (including herbal medications, supplements, or foods), as described, or use of a prohibited medication =\< 1 week prior to the start of study treatment
• •Any other condition that would, in the investigator?s judgment, contraindicate an individual?s participation in the clinical study due to safety concerns or compliance with clinical study procedures, e.g., infection/inflammation, intestinal obstruction, unable to swallow medication, social/ psychological issues, etc
• •Participants who have undergone major surgery (e.g., intracranial, intrathoracic, or intra-abdominal surgery) =\< 3 weeks prior to starting study drug or who have not recovered from side effects of such procedure
• •Participants that are pregnant or nursing (lactating)
• •Prisoners or individuals who are involuntarily incarcerated
• •Medical, psychiatric, cognitive or other conditions that may compromise the participant?s ability to understand the patient information, give informed consent, comply with the study protocol or complete the study