Ipilimumab and Imatinib Mesylate in Advanced Cancer

Inclusion Criteria: * For dose escalation study, patients must have histological confirmation of solid tumors that is metastatic or unresectable. For expansion cohorts, patients must have metastatic or unresectable gastrointestinal stromal tumor (GIST), melanoma, or uncategorized tumors with tumor biopsies that are positive for c-KIT mutations by polymerase chain reaction (PCR) or immunohistochemistry (IHC). For patients enrolled in the melanoma expansion cohort, only select KIT mutations will be eligible. Patients with mutations in exon 13 V654X, 14 T6701, 17 D816X and all exon 18 mutations will not be eligible for enrollment. * Patients who have completed previous therapies 4-weeks prior to (or within 5 drug half lives) enrollment on study. Radiation therapy wash out period will be 2 weeks. This includes an exception of patients with metastatic GIST tumors who are taking maintenance imatinib mesylate therapy. These patients are allowed to remain on imatinib mesylate therapy up to enrollment in this study. * Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \> 60%). * Leukocytes \> 3,000/mcL * Absolute neutrophil count \> 1,500/mcL * Platelets \> 100,000/mcL * Total bilirubin \< or = 2.0 mg/dL. (Does NOT apply to patients with Gilbert's syndrome) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 X institutional upper limit of …