Phase 1 Study of Pazopanib With GSK1120212 in Advanced Solid Tumors, Enriched With Patients With Differentiated Thyroid Cancer, Soft-tissue Sarcoma, and Cholangiocarcinoma

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.