PDR001 Combination Therapy for Radioiodine-Refractory Thyroid Cancer

Inclusion Criteria: * Cohort A Only: Confirmation in a CLIA certified laboratory that one of the patient's thyroid tumors (primary tumor, recurrent tumor, or metastases) does not possess a BRAFV600- mutation (non-V600- BRAF mutations, including BRAF translocations, may be included in this cohort). * Cohort A Only: Evidence of progressive disease (e.g. presence of new or growing lesion(s) on radiologic imaging and/or new or worsening tumor-related symptoms) within 14 months of study enrollment * Cohort B Only: Confirmation in a CLIA certified laboratory that one of the patient's thyroid tumors (primary tumor, recurrent tumor, or metastases) possesses a BRAFV600- mutation (e.g. V600E, V600K, V600D). * Cohort B Only: Patients must have documented progression (evidence of tumor growth or appearance of new tumor) on prior BRAF directed therapy (e.g. (but not limited to) vemurafenib, dabrafenib) and must have tolerated this therapy without \> Grade 3 toxicity on their most recent evaluation (excluding Grade 4 asymptomatic laboratory abnormalities). * Patients must have pathologically or cytologically confirmed differentiated thyroid cancer of follicular origin (including papillary thyroid carcinoma, follicular thyroid carcinoma, hurthle cell carcinomas, poorly differentiated thyroid carcinoma and their respective variants). * Patients must have RECIST v1.1 measurable disease. * Patients must have recurrent or metastatic disease not amenable to curative surgery or radiation. * Age \> 18 years. * ECOG performance status of 0 or 1. * Patients must have no recent treatment for thyroid cancer as defined as: * No prior RAI therapy is allowed \<6 months prior to initiation of therapy on this protocol. A diagnostic study using \<10 mCi of RAI is not considered RAI therapy * No external beam radiation therapy \<4weeks prior to initiation of therapy on this protocol. * No chemotherapy or targeted therapy (e.g., tyrosine kinase inhibitor) is allowed \<4 weeks prior to the initiation of therapy on this protocol (an exception to this are patients on dabrafenib who will be enrolling into Cohort B). Dabrafenib may be continued prior to and through trial enrollment into the start of the study therapy when PDR001 will be added to dabrafenib * RAI-refractory disease on structural imaging, defined as one of the following: * Total lifetime dose of radioiodine \> 600 mCi * A tumor that is not radioiodine-avid on a diagnostic radioiodine scan performed prior to enrollment in the current study. * A radioiodine-avid metastatic lesion which remained stable in size or progressed despite radioiodine treatment 6 months or more prior to study entry in the study. There are no size limitations for the index lesions used to satisfy this entry criterion * The presence of at least one fluorodeoxyglucose (FDG) avid lesion. * Patients must be able to swallow and retain orally-administered pills without any clinically significant gastrointestinal abnormalities that may alter absorption, such as malabsorption syndrome or major resection of the stomach or bowels. * Patients must have tissue from the primary tumor or metastases available for correlative studies. Either a paraffin block or at least 20 unstained slides are acceptable (30 unstained slides would be ideal). (If less than twenty unstained slides are available and a paraffin bloc is not available, the patient may be able to participate at the discretion of the investigator). * Patients must agree to undergo two research biopsies of (a) malignant lesion(s). Tumor tissue obtained prior to study consent or treatment as part of standard of care can also be submitted in lieu of performance of the first pre-treatment biopsy if the Principal Investigator deems it to be of sufficient quantity/quality/timeliness. Patients may be exempt from biopsy if 1) the investigator or person performing the biopsy judges that no tumor is accessible for biopsy, 2) the investigator or person performing the biopsy feels that the biopsy poses too great of a risk to the patient, or 3) the patient cannot be safely removed from anti-coagulation therapy (if the anti-coagulation therapy needs to be temporarily held for the biopsy procedure). If the only tumor accessible for biopsy is also the only lesion that can be used for RECIST v1.1 response evaluation, then the patient may be exempt from biopsy. If the investigator deems a second research biopsy to be high risk after a patient has completed the first research biopsy, the patient may be exempt from the second biopsy. * Screening laboratory values must meet the following criteria: * WBC ≥ 2000/µl * Neutrophils ≥ 1500/µl * Platelets ≥ 100 x 10\^3/µl * Hemoglobin \> 9.0 g/dL * AST/ALT ≤ 3 x ULN * Total Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL) * Serum creatinine ≤ 1.5 x ULN or creatinine clearance (CrCl) ≥ 40 mL/min (if using the Cockcroft-Gault formula below): Female CrCl = (140 - age in years) x weight in kg x 0.85/72 x serum creatinine in mg/dL Male CrCl = (140 - age in years) x weight in kg x 1.00/72 x serum creatinine in mg/dL * Left ventricular ejection fraction ≥ institutional lower limit of normal by transthoracic echocardiogram (ECHO) performed within 1 month of study drug initiation. Exclusion Criteria: * Cohort A Only: * Patients with the following ophthalmological finding/conditions: * Intraocular pressure \>21 mmHg, or uncontrolled glaucoma (irrespective of intraocular pressure). * Current or past history of central serous retinopathy or retinal vein occlusion. * Cohort A Only: Prior therapy with a MEK 1/2 targeted drug (with the exception of patients who received this therapy for a defined period of time to enhance radioiodine activity). * Symptomatic metastatic brain or leptomeningeal tumors (asymptomatic or treated metastatic brain or leptomeningeal tumors are allowed). * Prior therapy directed at the PD1/PD-L1 axis. * Any of the following cardiovascular risks: * A QT interval corrected for heart rate using the Bazett's formula QTcB ≥ 480 msec. * Clinically significant uncontrolled arrhythmias (Exception: patients with controlled atrial fibrillation for \>30 days prior to enrollment are eligible). * Acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months of enrollment. * ≥ Class II congestive heart failure as defined by the New York Heart Association (NYHA) functional classification system. * Treatment-refractory hypertension defined as a blood pressure of systolic \>140 mmHg and/or diastolic \>90 mmHg which cannot be controlled by anti-hypertensive therapy. * Prior malignancy if treated within 2 years of trial drug initiation (with the exception of non-melanoma skin cancers). Patients may be included if they have completed therapy for a prior malignancy \>2 years prior to drug initiation and are currently NED. * Use of any live vaccines against infectious diseases within 4 weeks of initiation of study treatment. * Systemic chronic steroid therapy (≥ 10mg/day prednisone or equivalent) or any immunosuppressive therapy (including but not limited to methotrexate, azathioprine, and TNF-alpha blockers) 7 days prior to planned first date of study treatment (note: topical, inhaled, nasal, intra-articular and ophthalmic steroids are allowed). * Active, known or suspected autoimmune disease or documented history of autoimmune disease with the exception of vitiligo, controlled type I diabetes mellitus on stable insulin, autoimmune thyroid disease or psoriasis not requiring systemic treatment. * Allogenic bone marrow or solid organ transplant. * History of severe hypersensitivity reactions to monoclonal antibodies or any other study drug components which in the opinion of the investigator may pose an increased risk of serious infusion reaction. * Known history of current interstitial lung disease or non-infectious pneumonitis. * Patients with active hepatitis B infection (HBV surface antigen positive). * Subject is known to be positive for Human Immunodeficiency Virus (HIV) or active Hepatitis C Virus (HCV). Testing for HIV or Hepatitis C prior to initiation of the study drug is not required. If a patient has a known history of treated HCV, then a viral load is required to confirm clearance of infection. * Pregnant or nursing (lactating) women confirmed by a positive hCG laboratory test within 72 hours prior to initiating study treatment. * Women of child-bearing potential (as defined in Appendix 18.3), unless they are using highly effective methods of contraception during dosing and for 150-days after stopping treatment with PDR001. Highly effective contraception methods include: * Total abstinence (when this is in line with the preferred and usual lifestyle of the patient). Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy), total hysterectomy, or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment * Male sterilization (at least 6 months prior to screening). The vasectomized male partner should be the sole partner for that patient * Use of oral, injected or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%), for example hormone vaginal ring or transdermal hormone contraception. NOTE: In case of use of oral contraception women should have been stable on the same pill for a minimum of 3 months before taking study treatment. * Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (i.e. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy), total hysterectomy, or tubal ligation at least six weeks ago. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential. * Sexually active males unless they use a condom during intercourse while on treatment and for 150 days after stopping treatment with PDR001 and should not father a child in this period. A condom is required to be used by vasectomized men as well during intercourse to prevent delivery of the drug via semen.