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

This phase II trial studies how well encorafenib and binimetinib given with or without nivolumab works in treating patients with BRAF V600 mutation positive thyroid cancer that has spread to other places in the body (metastatic) and does not respond to radioiodine treatment (refractory). Encorafenib and binimetinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Immunotherapy with monoclonal antibodies, such as nivolumab, may help the body?s immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. The trial aims to find out if the combination of encorafenib and binimetinib, with and without study nivolumab, is a safe and effective way to treat metastatic radioiodine refractory 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.

Eligibility Criteria:
Inclusion Criteria:

* Ability to understand and the willingness to sign a written informed consent document
* Histologically (or cytologically) confirmed diagnosis of metastatic, radioiodine (RAI) refractory, BRAFV600E/M mutant differentiated thyroid cancer (DTC)

  * Note: RAI refractoriness is defined as:

    * The absence of uptake of RAI on either a low-dose diagnostic whole body scan, or a post-treatment RAI scan in measurable lesions
    * Radiographic progression of disease within 12 months of the last course of RAI treatment, or
    * Having a cumulative lifetime administered dose of \> 600 mCi of RAI
* Measurable disease meeting the following criteria and confirmed by radiography review:

  * At least 1 lesion of \>= 1.0 cm in the longest diameter for a non-lymph node or \> 1.5 cm in the short-axis diameter for a lymph node metastasis that is serially measurable according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 using computed tomography/magnetic resonance imaging (CT/MRI). If there is only 1 target lesion and it is a non-lymph node, it should have a longest diameter of \>= 1.5 cm
  * Lesions that have had external beam radiotherapy or locoregional therapies such as radiofrequency (RF) ablation must show evidence of progressive disease based on RECIST 1.1 to be deemed a target lesion.
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 1
* Absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L
* Hemoglobin (Hgb) \>= 9 g/dL
* Platelets (PLT) \>= 75 x 10\^9/L
* Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN); participants with liver metastases =\< 5 x ULN
* Total bilirubin =\< 1.5 x ULN

  * Note: Individuals who have a total bilirubin level \> 1.5 x ULN will be allowed if their indirect bilirubin level is =\< 1.5 x ULN (i.e., participants with suspected or known diagnosis of Gilbert?s syndrome)
* Serum creatinine =\< 1.5 x ULN, or calculated creatinine clearance (determined as per Cockcroft-Gault) \>= 40 mL/min at screening
* Left ventricular ejection fraction (LVEF) \>= 50% as determined by a multigated acquisition (MUGA) scan or echocardiogram
* Triplicate average baseline corrected QT (QTc) interval =\< 480 ms
* Participants of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 72 hours prior to the start of assigned study intervention
* Participants of child-bearing potential agree to use highly effective methods of contraception starting with the first dose of assigned study intervention through 6 months after the last dose of study therapy
* Participants of childbearing potential are those who are not proven postmenopausal. Postmenopausal is defined as any of the following:

  * Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments
  * Luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels in the post-menopausal range for women under 50
  * Radiation-induced oophorectomy with last menses \> 1 year ago
  * Chemotherapy-induced menopause with \> 1 year interval since last menses
  * Surgical sterilization (bilateral oophorectomy or hysterectomy)
* Male participants must agree to use an adequate method of contraception starting with the first dose of study therapy through 6 months after the last dose of study therapy

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