COACH - Comparing Two Different Methods to Suppress Thyrotropin in Patients With Advanced Thyroid Cancer

Inclusion Criteria: 1. Minimum age of 18 years, with no upper limit of age. 2. ECOG 0-2 3. Patients must be capable of providing consent to enrollment and willing to comply with study treatment and follow-up. 4. Diagnosis of differentiated thyroid cancer (including papillary, follicular, oncocytic, and poorly differentiated subtypes) with advanced structural disease (defined as unresectable persistent/ recurrent locoregional disease and/or distant metastases). 5. Residence within Alberta and referral to the Cross Cancer Institute in Edmonton, for consideration of anticancer therapy and/or follow-up. 6. Absence of any condition hampering compliance with the study protocol and follow-up schedule; those conditions should be discussed with the patient before registration in the study. 7. Patients of childbearing / reproductive potential should use highly effective birth control methods, as defined by the investigator, during the study treatment period and for a period of 30 days after the last dose of study drug. A highly effective method of birth control is defined as those resulting in low failure rate (i.e., less than 1% per year) when used consistently and correctly. Note: abstinence is acceptable if this is established and preferred contraception for the patient. 8. Women of childbearing potential (WOCBP) must have a negative serum (or urine) pregnancy test at the time of screening. WOCBP is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy or bilateral salpingectomy) and is not postmenopausal. Menopause is defined as 12 months of amenorrhea in a woman over age 45 years in the absence of other biological or physiological causes. In addition, females under the age of 55 years must have a serum follicle stimulating hormone, (FSH) level \> 40 mIU/mL to confirm menopause. 9. Females must not be breastfeeding (timeframe: during study treatment period and for a period of 30 days after the last dose of the study drug). 10. Ability to obtain sufficient thyroid cancer tissue to conduct baseline NGS testing (could be fresh or archived tissue). Exclusion Criteria: 1. Recent acute coronary event (within 6 months of randomization). 2. History of atrial fibrillation. 3. Known hypersensitivity to levothyroxine. \- Treatment with other investigational drugs within 30 days prior to randomization. 4. History of fragility fractures or established diagnosis of osteoporosis. * Prior treatment with levothyroxine before study entry at any dose and with any TSH target is not an exclusion criterion.