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 normal (patients with liver involvement will be
             allowed < or = 5.0 X institutional upper normal limit)

          -  Serum creatinine < 2.0 mg/dL

          -  Patients MUST have recovered from all treatment related toxicities to grade 1 National
             Center Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) (version
             [v] 4.0) in severity.

          -  Patients must be willing and able to review, understand, and provide written consent
             before starting therapy.

          -  Patients with histologically proven intracranial glioblastoma, gliosarcoma or
             anaplastic astrocytoma will be eligible. Patients must have shown unequivocal
             radiographic evidence for tumor progression by magnetic resonance imaging (MRI) scan.
             A scan should be performed within 14 days prior to registration and on a steroid dose
             that has been stable for at least 5 days. If the steroid dose is increased between the
             date of imaging and registration, a new baseline MRI is required.

          -  Patients in the expansion cohort must also agree to participate in the biomarker
             study. However, patients in the melanoma KIT positive mutant subgroup, patients must
             agree to participate in the biomarker study and biopsies.

          -  Patients must be willing to stay within 2 hours drive of MD Anderson Cancer Center
             whilst receiving Ipilimumab therapy. Patient must also agree to present to MD Anderson
             emergency center while on Ipilimumab therapy.

        Exclusion Criteria:

          -  Autoimmune disease: Patients with a history of inflammatory bowel disease (including
             Crohn's disease and ulcerative colitis) and autoimmune disorders such as rheumatoid
             arthritis, systemic progressive sclerosis [scleroderma], systemic lupus erythematosus
             or autoimmune vasculitis [e.g., Wegener's granulomatosis] are excluded from this
             study.

          -  History of acute diverticulitis, intra-abdominal abscess, gastrointestinal (GI)
             obstruction, abdominal carcinomatosis or other known risk factors for bowel
             perforation.

          -  Any underlying medical or psychiatric condition, which in the opinion of the
             Investigator, will make the administration of study drug hazardous or obscure the
             interpretation of adverse events (AEs): e.g. a condition associated with frequent
             diarrhea or chronic skin conditions, recent surgery or colonic biopsy from which the
             patient has not recovered, or partial endocrine organ deficiencies.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, history of congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements.

          -  Known human immunodeficiency virus (HIV), hepatitis B, or hepatitis C.

          -  Any non-oncology live vaccine therapy used for prevention of infectious diseases (for
             up to one month prior to or after any dose of ipilimumab).

          -  Concomitant therapy with any of the following: IL-2, interferon or other non-study
             immunotherapy regimens; cytotoxic chemotherapy; immunosuppressive agents; other
             investigational therapies; or chronic use of systemic corticosteroids (when used in
             the management of cancers other than intracranial glioblastoma, gliosarcoma or
             anaplastic astrocytoma, or when used to treat non-cancer-related illnesses).

          -  Patients who do not agree to practice appropriate birth control methods while on
             therapy.

          -  Pregnant women are excluded from this study. Women of child-bearing potential and men
             must agree to use contraception prior to study entry and for the duration of study
             participation. Should a woman become pregnant or suspect she is pregnant while
             participating in this study, she should inform her treating physician.