Inclusion Criteria:

- Pathologically (histologically or cytologically) proven diagnosis of anaplastic
thyroid cancer (a diagnosis that is noted to be "consistent with anaplastic thyroid
cancer" with the presence of a thyroid mass is acceptable)

- If there was a total or partial thyroidectomy completed within 3 months of
enrollment, the surgical specimen must show the area of anaplastic thyroid cancer to
be at least 1 cm in greatest dimension

- No known brain metastases

- Zubrod performance status 0-2

- Absolute neutrophil count (ANC) >= 1,500 cells/mm^3

- Platelets >= 100,000 cells/mm^3

- Hemoglobin (Hgb) >= 9.0 g/dL (the use of transfusion or other intervention to achieve
Hgb >= 9.0 g/dL is acceptable)

- Total bilirubin < 1.5 x institutional upper limit of normal (ULN) (except for
patients with Gilbert syndrome and elevations of indirect bilirubin)

- Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) < 2.5 x
institutional ULN (patients who have both bilirubin > ULN and AST/ALT > ULN are not
eligible unless they have Gilbert syndrome and elevations of indirect bilirubin)

- Spot urine protein to creatinine ratio (UPCR) < 1 or a 24-hour urine protein
collection < 1 gm) within 10 days prior to registration

- Creatinine < 1.5 mg/dL or within normal institutional limits (if neither criteria is
met, the creatinine clearance must be > 50 mL/min^2 per either the Cockcroft-Gault
equation, Jeliffe method, or 12- or 24-hour urine collection)

- Documentation of the patient's history of QTc prolongation, family history of
prolonged QTc, and relevant cardiac disease

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use adequate contraception during and for at least 6 months of
completing study therapy

- Blood pressure < 140/90 within 10 days of registration (must be taken and recorded by
a health care professional)

- If the systolic blood pressure is > 140 and/or diastolic blood pressure is > 90
at the time of registration, the patient's blood pressure must be controlled

- Systolic blood pressure must be < 140 and diastolic blood pressure must be < 90
on at least 2 separate measurements prior to the start of treatment

- The treating physician must believe that this is feasible in order to enroll the
patient

- No known active invasive malignancy (except for nonmelanomatous skin cancer,
differentiated thyroid cancer, or the presence of prostate cancer confined to the
prostate with a PSA < 1 ng/mL for more than 6 months)

- No patients with any of the following cardiovascular conditions within the past 6
months:

- Cerebrovascular accident (CVA) or transient ischemic attack (TIA)

- Admission for unstable angina

- Cardiac angioplasty or stenting

- Coronary artery bypass graft surgery

- Pulmonary embolism, untreated deep venous thrombosis (DVT), or DVT that has been
treated with therapeutic anticoagulation for less than 6 weeks

- Arterial thrombosis

- Symptomatic peripheral vascular disease

- Class II-IV heart failure as defined by the New York Heart Association (NYHA)
functional classification system (a patient who has a history of class II heart
failure and is asymptomatic on treatment may be considered eligible for the
study)

- Patients with an arrhythmia are excluded

- Patients with atrial fibrillation, supraventricular tachycardia, or bradycardia are
eligible but these conditions must be well controlled with medication or a pacemaker

- No patients with any condition that may impair the ability to swallow or absorb oral
medications/investigational product including:

- Any lesion, whether induced by tumor, radiation, or other conditions, that makes
it difficult to swallow capsules or pills

- Prior surgical procedures affecting absorption including, but not limited to,
major resection of stomach or small bowel

- Active peptic ulcer disease

- Malabsorption syndrome

- No patients with any condition that may increase the risk of gastrointestinal
bleeding or gastrointestinal perforation, including:

- Active peptic ulcer disease

- Known intraluminal metastatic lesions

- Inflammatory bowel disease (e.g., ulcerative colitis, Crohn disease) or other
gastrointestinal conditions that increase the risk of perforation

- History of abdominal fistula, gastrointestinal perforation, or intra-abdominal
abscess within 28 days prior to beginning study treatment

- No history of hemoptysis within 30 days of registration

- Patients who have minimal bleeding from the mouth that is clearly not related to
a source in the lungs (i.e., surgery such as a non-lung biopsy) are eligible
only after good hemostasis has been documented

- No uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection or psychiatric illness/social situations that would limit compliance with
study requirements

- No prior allergic reaction to the study drug(s) involved in this protocol

- Patients with QTc prolongation defined as a QTc interval > 480 msecs or other
significant electrocardiogram (EKG) abnormalities are ineligible

- No human immunodeficiency virus (HIV)-positive patients on combination antiretroviral
therapy

- No concurrent St. John wort

- No prior systemic chemotherapy for anaplastic thyroid cancer

- No patients who have had chemotherapy or radiotherapy within 4 weeks of
registration (6 weeks for nitrosoureas or mitomycin C) prior to entering the
study or those who have not recovered from adverse events due to agents
administered > 4 weeks previously

- No patients receiving other investigational agents

- No prior radiotherapy to the region of the study cancer that would result in overlap
of radiation therapy fields

- No patients who require heparin (other than low-molecular weight heparin)

- Strong inducers of CYP3A4, such as rifampin, are strictly prohibited

- Strong inhibitors of CYP3A4, including grapefruit juice, are prohibited