Nivolumab Plus Ipilimumab in Thyroid Cancer

Inclusion * Metastatic, RAI refractory, differentiated thyroid cancer (including papillary and follicular thyroid cancer and their sub-types such as Hurthle cell thyroid cancer as well as poorly differentiated thyroid cancer), with progression within 13 months prior to study registration. RAI refractoriness is defined as absence of uptake of RAI on either a low-dose diagnostic test or a post-treatment RAI scan in measurable lesions or radiographic progression of disease within 12 months of the last course of RAI treatment despite the recorded uptake of RAI with that previous therapy or having a cumulative lifetime administered dose of greater than 600mCi. * Exploratory cohort: incurable medullary thyroid cancer with prior tyrosine kinase inhibitor (TKI) failure and progression within 13 months prior to enrollment (10 patients) and anaplastic thyroid cancer (7 patients) * Any number of lines of prior treatment are allowed * Any line of prior treatment for patients under 65y, over 65y must have at least one prior line of TKI treatment * Age 18 years or older * ECOG performance status ≤2 (Karnofsky ≥60%, see Appendix A) * Participants must have normal organ and marrow function as defined below: * Screening laboratory values must meet the following criteria and should be obtained within 21 days prior to randomization/registration * WBC ≥ 2000/μL * Neutrophils ≥ 1500/μL * Platelets ≥ 100 x103/μL * Hemoglobin \> 9.0 g/dL * Serum creatinine ≤ 1.5 x ULN or creatinine clea…