Trametinib in Combination With Paclitaxel in the Treatment of Anaplastic Thyroid Cancer

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of anaplastic thyroid cancer (a diagnosis that is noted to be consistent with anaplastic thyroid cancer is acceptable). * Metastatic disease or local-regional disease that is considered not resectable for cure. * Patients must have measurable disease per RECIST v1.1 criteria, 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, MRI, or calipers by clinical exam * Age ≥18 years * ECOG performance status ≤2 (or Karnofsky ≥60) * Able to swallow and retain orally-administered medication and does not have any clinically significant gastrointestinal abnormalities that may alter absorption, such as malabsorption syndrome or major resection of the stomach or bowels * No CTCAE v4 grade \>2 neuropathy * Patients must have normal organ and marrow function as defined below: * Absolute neutrophil count (ANC) ≥1.5x10\^9/L * Hemoglobin ≥9 g/dL * Platelets ≥100x10\^9/L * Serum bilirubin ≤1.5x institutional upper limit of normal (ULN) (Unless Gilbert's Disease in which case total bilirubin ≤3x institutional ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤2.5x institutional ULN (≤5x institutional ULN if there is liver metastasis) * Serum creatinine ≤1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault formula) ≥50 mL/min OR 24-hour urine creatinine clearance ≥50 mL/min * Left ventricular ejection fraction ≥ institutional lower limit of normal (LLN) by ECHO or MUGA * Negative pregnancy test (serum or urine) within 14 days of registration in women of child-bearing potential. Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of trametinib administration * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 7 days of starting treatment. * Symptomatic or untreated brain metastases, leptomeningeal disease, or spinal cord compression * History of interstitial lung disease or pneumonitis * History or current evidence/risk of retinal vein occlusion (RVO) or central serous retinopathy (CSR): * History of RVO or CSR, or predisposing factors to RVO or CSR (e.g., uncontrolled glaucoma or ocular hypertension) * Visible retinal pathology as assessed by ophthalmic exam that is considered a high risk factor for RVO or CSR such as evidence of new optic disc cupping, evidence of new visual field defects, and intraocular pressure \>21 mm Hg * History or evidence of cardiovascular risk including any of the following: * LVEF\<LLN * A QT interval corrected for heart rate using the Bazett's formula QTcB ≥480 msec * History or evidence of current clinically significant uncontrolled arrhythmias (exception: patients with controlled atrial fibrillation for \>30 days prior to -enrollment are eligible) * History of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to randomization * History or evidence of current ≥ Class II congestive heart failure as defined by the New York Heart Association (NYHA) functional classification system * Treatment-refractory hypertension defined as a blood pressure of systolic \>150 mmHg and/or diastolic \>90 mmHg which cannot be controlled by anti-hypertensive therapy * Known cardiac metastases * Known Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV), or Hepatitis C Virus (HCV) infection (with the exception of chronic or cleared HBV and HCV infection, which will be allowed) HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with trametinib. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Any condition that may impair the ability to absorb oral medications/investigational product including: prior surgical procedures affecting absorption including, but not limited to major resection of stomach or small bowel; active peptic ulcer disease; and malabsorption syndrome * Any major surgery within 21 days prior to enrollment. * Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to taxanes and drugs chemically related to trametinib, or excipients or to dimethyl sulfoxide (DMSO) * Current use of a prohibited medication. The following medications or non-drug therapies are prohibited: * Concurrent treatment with bisphosphonates is permitted; however, treatment must be initiated prior to the first dose of study therapy. Prophylactic use of bisphosphonates in patients without bone disease is not permitted, except for the treatment of osteoporosis * Because the composition, 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)