Brief Summary: This phase I trial studies the side effects and best dose of ipilimumab and imatinib mesylate in treating patients with solid tumors that have spread to other places in the body or cannot be removed by surgery. Immunotherapy with monoclonal antibodies, such as ipilimumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Imatinib mesylate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving ipilimumab and imatinib mesylate may work better in treating patients with solid tumors.

Detailed Description: PRIMARY OBJECTIVES: I. To evaluate the safety and toxicity profile of intravenous ipilimumab (Yervoy) administered in combination with oral imatinib mesylate (GLEEVEC) for patients with advanced malignancies that are refractory to standard therapy, relapsed after standard therapy, or have no available standard therapy. II. To determine the maximum toxic dose (MTD) and dose limiting toxicities (DLT) of ipilimumab and imatinib mesylate combination therapy. SECONDARY OBJECTIVES: I. To determine antitumor activity of ipilimumab and imatinib mesylate combination therapy. II. To determine antitumor activity of ipilimumab and imatinib mesylate combination therapy in KIT confirmed solid tumors. III. To evaluate the potential predictive role of tumor-associated immune biomarkers for therapy effectiveness. IV. To evaluate the potential predictive role of therapy associated toxicities with antitumor activity. OUTLINE: This is a dose-escalation study. Patients receive ipilimumab intravenously (IV) over 90 minutes on day 1 and imatinib mesylated orally (PO) twice daily (BID) on days 1-21. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.