Study of Dabrafenib +/- Trametinib in Combination With Ipilimumab for V600E/K Mutation Positive Metastatic or Unresectable Melanoma

Inclusion Criteria: * Signed written informed consent * Males and females \>= 18 years of age * Histologically confirmed cutaneous melanoma that is either Stage IIIc (unresectable) or Stage IV (metastatic), and determined to be BRAF V600E or V600K mutation-positive by the local laboratory. Subjects with ocular or mucosal melanoma are not eligible * Measurable tumor by physical or radiographic examination * Subjects must not have had more than 1 previous treatment regimen with chemotherapy, interferon, or IL-2 for metastatic melanoma * All prior anti-cancer treatment-related toxicities (except alopecia) must be \<= Grade 1 according to the Common Terminology Criteria for Adverse Events (CTCAE) version 4.0 at the time of enrollment * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Adequate baseline organ function as defined by: absolute neutrophil count (ANC) \>= 1.2 × 109/L; Hemoglobin \>= 9 g/dL; Platelet count \>= 100 x 109/L; prothrombin time (PT) / international normalized ratio (INR) and partial thromboplastin time (PTT) \<= 1.5 x upper limit of normal (ULN); Albumin \>= 2.5 g/dL; Total bilirubin \<= 1.5 x ULN; aspartate aminotransferase (AST) and alanine transaminase (ALT) \<= 2.0 x ULN; Creatinine \<=1.5 mg/mL; Left Ventricular Ejection fraction (LVEF) \>= lower limit of normal (LLN) by ECHO * Women of childbearing potential must have a negative serum pregnancy test within 7 days prior to randomization and agree to use effective contraception, during the study, and for 30 days after the last dose of study treatment * Men with a female partner of childbearing potential must have either had a prior vasectomy or agree to use effective contraception for at least 2 weeks prior to the first dose of study treatment until 16 weeks after the last dose of study treatment to allow for clearance of any altered sperm * Able to swallow and retain orally administered study treatment and does not have any clinically significant gastrointestinal abnormalities that may alter absorption such as malabsorption syndrome or major resection of the stomach or bowels Exclusion Criteria: * Prior treatment with a BRAF inhibitor (including but not limited to dabrafenib, vemurafenib, and XL281/BMS-908662) or a MEK inhibitor (including but not limited to trametinib, AZD6244, and RDEA119) or ipilimumab or any other agent targeting a T-cell immunomodulatory pathway (including, but not limited to CTLA-4, PD-1, 4-1BB, OX40, GITR, CD27, and CD28) * Any major surgery, extensive radiotherapy, chemotherapy with delayed toxicity, biologic therapy, or immunotherapy within 21 days prior to randomization and/or daily or weekly chemotherapy without the potential for delayed toxicity within 14 days prior to randomization * Known Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV), or Hepatitis C Virus (HCV) infection (with the exception of chronic or cleared HBV and HCV infection) * A history of glucose-6-phosphate dehydrogenase (G6PD) deficiency * Brain metastasis are excluded unless 1. All known lesions were previously treated with surgery or stereotactic surgery (whole-brain radiation is not allowed unless given after definitive treatment with surgery or stereotactic surgery) AND 2. Brain lesion(s), if still present, must be confirmed stable (i.e., no increase in lesion size) for \>= 6 weeks prior to randomization (stability must be confirmed with two consecutive magnetic resonance image (MRI) or computed tomography (CT) scans with contrast, AND 3. Asymptomatic with no corticosteroid requirements for \>= 4 weeks prior to randomization, AND 4. No enzyme inducing anticonvulsants for \>= 4 weeks prior to randomization * A history or evidence of cardiovascular risk including any of the following 1. LVEF \< LLN for the institution 2. A corrected QT interval \>=480 msec (e.g. Bazett's formula \[QTcB\]) 3. A history or evidence of current clinically significant uncontrolled arrhythmias (exception: subjects with controlled atrial fibrillation for \> 30 days prior to randomization are eligible) 4. A history (within 6 months prior to first dose of study treatment) of acute coronary syndromes (including myocardial infarction or unstable angina), coronary angioplasty 5. A history or evidence of current \>=Class II congestive heart failure as defined by the New York Heart Association (NYHA) 6. Treatment refractory hypertension defined as systolic blood pressure \>140 millimetres of mercury (mmHg) and/or diastolic blood pressure \>90 mmHg which cannot be controlled by antihypertensive therapy 7. Patients with intra-cardiac defibrillators 8. Abnormal cardiac valve morphology (\>=grade 2) documented by echocardiogram (subjects with grade 1 abnormalities \[i.e., mild regurgitation/stenosis\] can be entered on study). Subjects with moderate valvular thickening should not be entered on study * A history or current evidence/risk of retinal vein occlusion (RVO) or Central serous retinopathy (CSR) including 1. Presence of predisposing factors to RVO or CSR (e.g., uncontrolled glaucoma or ocular hypertension, uncontrolled hypertension, uncontrolled diabetes mellitus, or a history of hyperviscosity or hypercoagulability syndromes), or 2. Visible retinal pathology as assessed by ophthalmic examination that is considered a risk factor for RVO or CSR such as evidence of new optic disc cupping; Evidence of new visual field defects on automated perimetry; Intraocular pressure \>21 mmHg as measured by tonography * History of any of the following diseases: inflammatory bowel disease or any other autoimmune bowel disease; systemic lupus erythematosus; rheumatoid arthritis; or any autoimmune ocular diseases. Patients with active autoimmune disease or a history of autoimmune disease other than those mentioned above must be approved by the GSK medical monitor * Active pneumonitis or interstitial lung disease * Lactating female * History of another malignancy (Exception: Subjects who have been disease-free for 3 years, or subjects with a history of completely resected non-melanoma skin cancer or successfully treated in situ carcinoma are eligible) * Any serious and/or unstable pre-existing medical, psychiatric disorder or other conditions that could interfere with subject's safety, obtaining informed consent or compliance to the study procedures * Any prohibited medication * Administration of an investigational study treatment within 28 days or 5 half-lives, whichever is longer, preceding the first dose of study treatment(s) in this study * Known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to the study treatments, their excipients, and/or dimethyl sulfoxide (DMSO) * Unwillingness or inability to follow the procedures outlined in the protocol