Testing the Combination of Cabozantinib, Nivolumab, and Ipilimumab (CaboNivoIpi) for Advanced Differentiated Thyroid Cancer

Exclusion Criteria

• •Patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1
• •Patients must have radioactive iodine (RAI)-refractory/resistant disease as defined by one or more of the following criteria:
• •* One or more measurable lesions that do not demonstrate RAI uptake,
• •* Progressive disease (PD) (new lesion or progression of previously known lesions), as defined by RECIST v1.1, within 12 months of prior RAI therapy,
• •* One or more measurable lesion present after cumulative RAI dose of \> 600 mCi, or
• •* Fluorodeoxyglucose (FDG)-positron emission tomography (PET) scan-positive disease (SUV \>= 5 in tumor lesion)
• •The patient's disease must have progressed on one line of VEGFR-targeted therapy (including, but not limited to, sorafenib, sunitinib, vandetanib, pazopanib, or lenvatinib, etc.) as defined by PD per RECIST v1.1 while receiving VEGFR-targeted therapy. Patients who have received more than one line of prior VEGFR-targeted therapy will not be eligible
• •Prior external beam radiation to extra-osseous disease, systemic cytotoxic chemotherapy or BRAF- or non-VEGFR-targeted therapies will be allowed, provided that \> 4 weeks has elapsed since receiving prior treatment. Radiation to bone metastases is allowed up to 2 weeks prior to initiation of study treatment
• •Patients must be \>= 18 years of age. Because no dosing or adverse event data are currently available on the use of XL184 (cabozantinib), nivolumab, or ipilimumab in patients \<18 years of age, children are excluded from this study, but may be eligible for future pediatric trials.
• •Patients must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
• •Patients must have recovered to baseline or =\< Common Terminology Criteria for Adverse Events (CTCAE) v5.0 grade 1 from toxicities related to any prior treatments, unless adverse event (AE)(s) are clinically nonsignificant and/or stable on supportive therapy
• •Absolute neutrophils \>= 1,500/mcL
• •Platelets \>= 100,000/mcL
• •Hemoglobin \>= 9 g/dL
• •Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN); =\< 3.0 x ULN for patients with Gilbert's syndrome
• •Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3.0 x institutional ULN
• •Alkaline phosphatase =\< 3.0 x institutional ULN; =\< 5.0 x ULN with documented bone metastases
• •Creatinine =\< 1.5 x ULN OR creatinine clearance (CrCl) \>= 50 mL/min (if using the Cockcroft-Gault formula)
• •Serum albumin \>= 2.8 g/dL
• •Lipase \< 2.0 x ULN and no radiologic or clinical evidence of pancreatitis
• •Urine protein/creatinine ratio (UPCR) =\< 1 mg/mg
• •Serum phosphorus, calcium, magnesium, and potassium within institutional normal limits
• •Prothrombin time (PT)/international normalized ratio (INR) and partial thromboplastin time (PTT) test \< 1.3 x ULN
• •Patients with a history of human immunodeficiency virus (HIV) infection must be on an effective anti-retroviral regimen utilizing agents that do not strongly induce or inhibit cytochrome P450 (CYP) 3A4, and must have an undetectable viral load measured within 6 months prior to study registration
• •Patients with evidence of chronic hepatitis B virus (HBV) infection must have undetectable HBV viral load on suppressive therapy, if indicated
• •Patients must not have had prior treatment with XL184 (cabozantinib), any MET-targeting tyrosine kinase inhibitor (TKI), or any MET-targeting monoclonal antibody (MetMAb), such as onartuzumab
• •Patients must not have had prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T cell co-stimulation or immune checkpoint pathways
• •Patients must not have a tumor invading or encasing any major blood vessels, and must not have evidence of tumor invading the gastrointestinal (GI) tract (esophagus, stomach, small or large bowel, rectum, or anus), or any evidence of endotracheal or endobronchial tumor within 28 days before the first dose of XL184 (cabozantinib)
• •Patients must not have a diagnosis of another malignancy within 2 years before the first dose of study treatment, except for superficial skin cancers, or localized, low grade tumors deemed cured and not treated with systemic therapy. Adjuvant hormonal therapy for history of prostate or breast cancer is allowed
• •Patients must not have received cytotoxic chemotherapy (including investigational cytotoxic chemotherapy) or biologic agents (e.g., cytokines or antibodies) within 4 weeks, or nitrosoureas/ mitomycin C within 6 weeks, before the first dose of study treatment. Patients may continue on bone-modifying agents (denosumab or bisphosphonates) with caution
• •Patients must not have received radiation therapy:
• •* To the thoracic cavity, abdomen, or pelvis within 4 weeks before the first dose of study treatment;
• •* To bone metastases within 14 days before the first dose of study treatment;
• •* To any other sites within 4 weeks before the first dose of study treatment
• •Patients must not have clinically relevant, ongoing complications from prior radiation therapy. Palliative (limited-field) radiation therapy is permitted as long as the patient does not have disease progression according to RECIST v 1.1
• •Patients must not have received any type of small molecule kinase inhibitor (including investigational kinase inhibitors) within 4 weeks before the first dose of study treatment
• •Patients must not have received any other type of investigational agent within 4 weeks before the first dose of study treatment
• •Patients must not have a corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 msec by electrocardiogram (EKG) within 28 days before the first dose of study treatment
• •* Note: if a single EKG shows a QTcF with an absolute value \> 500 msec, two additional EKGs at intervals of approximately 3 min must be performed within 30 min after the initial EKG, and the average of these three consecutive results for QTcF will be used to determine eligibility
• •Pregnant women are excluded from this study because XL184 (cabozantinib) has the potential for teratogenic or abortifacient effects, and the effects of nivolumab and ipilimumab on the developing fetus are not well known. Because there is an unknown but potential risk for AEs in nursing infants secondary to treatment of the mother, breastfeeding must be discontinued if the mother is treated with XL184 (cabozantinib), nivolumab, or ipilimumab
• •Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including high dose systemic corticosteroids, should be excluded. These include but are not limited to: immune-related neurologic disease, such as multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, or myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, or autoimmune hepatitis. Patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded because of the risk of recurrence or exacerbation of disease. Patients with vitiligo, type I diabetes mellitus (DM), or endocrine deficiencies (e.g., thyroiditis) managed with replacement hormones, including physiologic corticosteroids, are eligible
• •Patients with rheumatoid arthritis and other arthropathies, Sjogren's syndrome and psoriasis controlled with topical medication, and patients with positive serology, (e.g., antinuclear antibodies \[ANA\] or anti-thyroid antibodies) should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible