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