Study of Everolimus and Sorafenib in Patients With Advanced Thyroid Cancer Who Progressed on Sorafenib Alone

Inclusion Criteria: * Diagnosis of thyroid cancer, that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective. * All patients will have been required to have had sorafenib for entry and have had documented progression while on previous treatment with sorafenib. * Measurable disease defined as at least one malignant lesion that can be accurately measured on computerized tomography (CT) and/or magnetic resonance imaging (MRI) scan. * ECOG performance status \< 2. * Life expectancy greater than 3 months. * Intellectual, emotional, and physical ability to comply with oral medication. Exclusion Criteria: * Restrictions regarding certain prior treatments will apply. * Significant medical disease including: uncontrolled congestive heart failure; active symptoms of coronary artery disease, uncontrolled seizure disorder; active infection; uncontrolled diabetes mellitus; requirement for chronic high dose corticosteroid treatment (Topical or inhaled corticosteroids are allowed); requirement for concurrent immunosuppressive drug(s); active autoimmune disease. * Organ allografts. * Known HIV-infection (HIV testing is not required for participation). * Pregnant or breast feeding. Women of childbearing potential and sexually active males must be advised to take precautions to prevent pregnancy during treatment * History of second cancer (except adequately treated basal cell or squamous cell skin cancer, in situ treated cervical cancer, colon cancer or melanoma, or any other cancer for which the patient has been disease-free for three or more years). * Known hypersensitivity to everolimus or other rapamycins (e.g., sirolimus, temsirolimus) or to its excipients * Use of any experimental therapy within 4 weeks prior to baseline evaluations done prior to enrollment (with the exception of sorafenib which may be continued until treatment start). Therefore, all experimental treatments other than sorafenib must be discontinued 4 weeks prior to baseline studies or enrollment. * Patients who did not previously tolerate sorafenib at 200 mg once daily are excluded from the study.