The purpose of this study is to determine the safety and toxicity of the combination of pazopanib and GSK1120212 in patients with solid tumors and identify the maximum tolerated dose (MTD) of this combination for phase II study.

Inclusion Criteria:

• Dose escalation cohort for all solid tumors is closed to enrollment.
• Expansion cohorts: Soft-tissue sarcoma, cholangiocarcinoma, and differentiated thyroid cancer (DTC) cohorts are closed to enrollment. Patients in the DTC cohort must have disease that is able to be biopsied.
• Must have measurable disease.
• Tumor progression in the 6-month period prior to study drug initiation.
• DTC patients: must have radioiodine non-avid lesions, OR radioiodine avid lesions that have not responded to treatment with radioactive iodine.
• ECOG performance status less than or equal to 1.
• Life expectancy >3 months.
• Blood pressure <140 mmHg and <90 mmHg.
• LVEF is >= 50%
• Must be able to swallow pills.

Exclusion Criteria:

• Chemotherapy, radiotherapy, other investigational therapy, or major surgery within 4 weeks.
• Sarcoma and cholangiocarcinoma ONLY: Prior VEGF-targeted TKI therapy.
• Pregnant or currently breastfeeding.
• Unresolved toxicity greater than grade 1.
• Evidence of active hepatitis or HIV.
• Significant cardiovascular disease.
• Taking medications known to be strong inducers or inhibitors of CYP3A enzymes.
• Clinically significant gastrointestinal abnormalities that may increase the risk for gastrointestinal bleeding.
• History of gastrointestinal condition causing malabsorption or obstruction.
• Cerebrovascular accident including transient ischemic attack (TIA), pulmonary embolism or untreated deep vein thrombosis (DVT) within past 6 months.
• Known endobronchial lesions and/or lesions infiltrating major pulmonary vessels that increase risk of pulmonary hemorrhage.
• Hemoptysis within 6 months of starting treatment.
• History of retinal vein occlusion (RVO) or central serous retinopathy (CSR), or predisposing factors to RVO or CSR as assessed by ophthalmic exam.
• Known brain mets that are not stable for at least 8 weeks prior to treatment, or patient is on glucocorticoids for brain mets.