Patient description: A 16-year-old girl came to the clinic complaining of weight gain and abnormal menstrual cycles. Her BMI was 24, but she has gained 5 kg in the past few weeks. She gets tired more frequently and does not have energy to go dancing with her friends. Her lab results were remarkable for high TSH levels (15 mU/L) and low free T4 levels (0.18 ng/dl). Her anti-TPO levels were extremely high (136 IU/ml). She was diagnosed with Hashimoto disease. She does not smoke and she is not sexually active.

Clinical trial eligibility criteria: eligible ages (years): 18.0-999.0,  Metastatic Thyroid Gland Carcinoma Poorly Differentiated Thyroid Gland Carcinoma Recurrent Thyroid Gland Carcinoma Refractory Thyroid Gland Carcinoma Stage IV Thyroid Gland Follicular Carcinoma AJCC v7 Stage IV Thyroid Gland Papillary Carcinoma AJCC v7 Stage IVA Thyroid Gland Follicular Carcinoma AJCC v7 Stage IVA Thyroid Gland Papillary Carcinoma AJCC v7 Stage IVB Thyroid Gland Follicular Carcinoma AJCC v7 Stage IVB Thyroid Gland Papillary Carcinoma AJCC v7 Stage IVC Thyroid Gland Follicular Carcinoma AJCC v7 Stage IVC Thyroid Gland Papillary Carcinoma AJCC v7 Patients must have histologically or cytologically confirmed thyroid carcinoma of follicular origin (including papillary, follicular, or poorly differentiated subtypes and their respective variants); confirmation of thyroid carcinoma will be done at Memorial Sloan-Kettering (MSK) Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as >= 20 mm with conventional techniques or as >= 10 mm with spiral CT scan, magnetic resonance imaging (MRI), or calipers by clinical exam; tumors in previously irradiated fields may be considered measurable if there is evidence of tumor progression after radiation treatment RAI-refractory disease on structural imaging, defined as any one of the following A metastatic lesion that is not radioiodine-avid on a diagnostic radioiodine scan performed prior to enrollment in the current study, or A radioiodine-avid metastatic lesion which remained stable in size or progressed despite radioiodine treatment 6 months or more prior to entry in the study; there are no size limitations for the index lesion used to satisfy this entry criterion The presence of at least one fluorodeoxyglucose (FDG) avid lesion 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 millicurie (mCi) of RAI is not considered RAI therapy No external beam radiation therapy < 4 weeks prior to initiation of therapy on this protocol; (previous treatment with radiation for any indication is allowed if the investigator judges that the previous radiation does not significantly compromise patient safety 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  History of another malignancy; exception: patients who have been disease-free for 3 years, patients with a history of completely resected non-melanoma skin cancer, and/or patients with indolent secondary malignancies, are eligible; MSK can consult the Cancer Therapy Evaluation Program (CTEP) Medical Monitor if unsure whether second malignancies meet the requirements specified above History of interstitial lung disease or pneumonitis Use of other investigational drugs within 28 days (or five half-lives, whichever is shorter; with a minimum of 14 days from the last dose) preceding the first dose of trametinib and during the study Symptomatic or untreated leptomeningeal or brain metastases or spinal cord compression Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO) or to thyrotropin alpha (Thyrogen) Current use of a prohibited medication; the following medications or non-drug therapies are prohibited Other anti-cancer therapy while on study; (note: megestrol [Megace] if used as an appetite stimulant is allowed; thyroid-stimulating hormone [TSH] suppressive therapy is also allowed; palliative radiation therapy to non-target lesions is also allowed) Concurrent treatment with bisphosphonates is permitted; prophylactic use of bisphosphonates in patients without bone disease is not permitted, except for the treatment of osteoporosis Because the composition, pharmacokinetics (PK), and metabolism of many herbal supplements are unknown, the concurrent use of all herbal supplements is prohibited during the study (including, but not limited to, St. John's wort, kava, ephedra [ma huang], gingko biloba, dehydroepiandrosterone [DHEA], yohimbe, saw palmetto, or ginseng) Patients with the following ophthalmological findings/conditions