Cyclophosphamide and Sirolimus for the Treatment of Metastatic, RAI-refractory, Differentiated Thyroid Cancer

Inclusion Criteria: * Histologically documented differentiated thyroid cancer with or without metastases, not amenable to curative treatment; or the patient has documented refusal of curative treatment * Measurable disease (\>10 mm) and have progression of disease based on RECIST criteria. Previously irradiated tumor lesions are not considered measurable unless they have progressed since radiation. * Previous failure of Iodine-131 (131I) therapy or not candidates to receive 131I as assessed by treating physician. * Age ≥ 18 years * ECOG (Eastern Cooperative Oncology Group) performance status 0-2 * Life expectance of ≥ 12 weeks * 131I therapy not allowed within 24 weeks before entry (4 weeks if negative post-treatment scan) * Adequate organ and marrow function * Women of childbearing potential must have a negative serum or urine pregnancy test within 3 days prior to treatment * Signed and dated informed consent document indicating that the patient (or legally acceptable representative) has been informed of all pertinent aspects of the trial prior to enrollment * Willingness and ability to comply with scheduled visits, treatment plans, including willingness to take study medication, laboratory tests, and other study procedures Exclusion Criteria: * Inability to obtain Foundation One testing on archival tissue, or, lack of previous Next Generation Sequencing * Chemotherapy, tyrosine kinase inhibitor, or radiation therapy within 4 weeks * Prior experimental therapy within 4 weeks of planned start of this trial * 131I therapy within 24 weeks before entry (4 weeks if negative post-treatment scan) * Previous treatment with an mTOR inhibitor * Patients who are currently receiving treatment with strong inhibitors or inducers of CYP3A4 or P-glycoprotein that cannot be discontinued at least one week prior to the start of treatment with Cyclophosphamide and Sirolimus * Impairment of GI (gastrointestinal) function or GI disease that may significantly alter the absorption of study medications (e.g., ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, small bowel resection) including dependence on a G-Tube for administration of medications. * A serious uncontrolled medical disorder or active infection that would impair their ability to receive study treatment * Patients with known sensitivities to either cyclophosphamide and/or sirolimus * Patients with known urinary outflow obstruction * Dementia or significantly altered mental status that would prohibit the understanding or rendering of informed consent and compliance with the requirements of this protocol * Patients (male and female) having procreative potential who are not willing or not able to use adequate contraception or practicing abstinence * Women who are pregnant or breast-feeding * Patients residing in prison