INCB039110 in Combination With Dabrafenib and Trametinib in Patients With BRAF-mutant Melanoma and Other Solid Tumors.

Inclusion Criteria: * For Dose-Escalation Phase: Patients must have histologically confirmed, BRAF-mutant (V600E/K) malignancy (molecularly confirmed using Cobas assay or a comparable FDA-approved assay (for exceptions, see below\*) that is metastatic or unresectable, have received and tolerated prior BRAF or BRAF and MEK inhibitor (BRAF targeted) therapy or not previously received BRAF targeted therapy, and for which standard curative or palliative measures do not exist or are no longer effective. * If test at CLIA-certified lab used a non-FDA approved method, information about the assay must be provided to the Overall Principal Investigator (PI) for approval. (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test). * For Dose-Expansion Phase: Patients must have histologically confirmed, BRAF-mutant (V600E/K) melanoma (molecularly confirmed using Cobas assay or a comparable FDA-approved assay (for exceptions, see below\*) that is metastatic or unresectable, have received and tolerated prior BRAF or BRAF and MEK inhibitor (BRAF targeted) therapy at full dose or not previously received BRAF targeted therapy. * If test at CLIA-certified lab used a non-FDA approved method, information about the assay must be provided to the Overall Principal Investigator (PI) for approval. (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test). * Patients must have measurable disease by RECIST, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥20 mm with conventional techniques or as ≥10 mm with spiral CT scan, MRI, or calipers by clinical exam. See Section 11 for the evaluation of measurable disease. * Patients may have received any number of prior lines of therapy. All prior systemic anti-cancer treatment-related toxicities must be less than or equal to Grade 1 according to the Common Terminology Criteria for Adverse Events version 4 (CTCAE version 4.0; NCI, 2009) at the time of enrollment. This does not include alopecia and Grade 2 or less peripheral neuropathy. * Age ≥18 years. Because no dosing or adverse event data are currently available on the use of INCB039110 in combination with dabrafenib and trametinib in patients \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. * ECOG performance status ≤1 (Karnofsky ≥70%, see Appendix A). * Life expectancy of greater than 3 months in the opinion of the investigator. * Patients must have acceptable organ and marrow function as defined below: * Leukocytes (WBCs) ≥3,000/uL * absolute neutrophil count ≥1,500/uL * hemoglobin \> 9 g/dl (patients may be transfused to this level) * platelets ≥ 100,000/uL * total bilirubin \< 1.5 x institutional upper limit of normal OR \> 1.5 x institutional upper limit of normal allowed if direct bilirubin is within normal range. * AST(SGOT)/ALT(SGPT) ≤ 2.5 x institutional upper limit of normal * PT/INR and PTT \< 1.3 x ULN1 * Serum creatinine ≤1.5 mg/dL OR creatinine clearance ≥50 mL/min/1.73 m2 * Potassium \>3 and \<5.5mmol/L * Magnesium \>1.2 and \<2.5 mg/dL * 1Therapeutic levels of anti-coagulation are permitted if clinically indicated, as per section 3.2.15. Thus PT/INR may be \>1.3 if therapeutically anti-coagulated. * The effects of INCB039110, dabrafenib, and trametinib on the developing human fetus are unknown. For this reason, women of child-bearing potential must have a negative serum pregnancy test within 14 days prior to registration and agree to use effective contraception (barrier method of birth control, or abstinence; hormonal contraception is not allowed due to drug-drug interactions which can render hormonal contraceptives ineffective) from 14 days prior to registration, throughout the treatment period, and for 4 months after the last dose of study treatment. Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. * Based on studies in animals, it is also known that dabrafenib may cause damage to the tissue that makes sperm. This may cause sperm to be abnormal in shape and size and could lead to infertility, which may be irreversible. * Men with a female partner of childbearing potential must have either had a prior vasectomy or agree to use effective contraception. Additionally, male subjects (including those who are vasectomized) whose partners are pregnant or might be pregnant must agree to use condoms for the duration of the study and for 4 months following completion of therapy. * Ability to understand and the willingness to sign a written informed consent document. * Able to swallow and retain oral medication, and must 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: * Patients who received prior systemic anti-cancer therapy (chemotherapy with delayed toxicity, extensive radiotherapy, immunotherapy, biologic therapy, or vaccine therapy) within the last 3 weeks prior to Day 1 of Cycle 1. Patients are permitted to be on dabrafenib and trametinib at start of therapy without wash-out period prior to Day 1 of Cycle 1. Dosing will change to protocol determined dose levels on Day 1 of Cycle 1 * Patients must not have received prior JAK1 inhibitor therapy. * Patients who are receiving any other investigational agents. Patients who have taken an investigational drug within 28 days or 5 half-lives (minimum 14 days), whichever is shorter, prior to registration. * Patients with history of RAS mutation-positive tumors are not eligible regardless of interval from the current study. Prospective RAS testing is not required. However, if the results of previous RAS testing are known, they must be used in assessing eligibility. * Patients must have no clinical evidence of leptomeningeal or brain metastasis causing spinal cord compression that are symptomatic, untreated, not stable for ≥ 4 weeks prior to Day 1 of Cycle 1 (must be documented by imaging), or requiring corticosteroids to manage metastasis-related symptoms. Subjects who have been off of corticosteroids for at least 2 weeks prior to Day 1 of Cycle 1 or are on a stable dose of ≤10 mg per day of a prednisone equivalent for \>1 month prior to Day 1 of Cycle 1 can be enrolled. Subjects must also be off of enzyme-inducing anticonvulsants for \>4 weeks prior to Day 1 of Cycle 1. * History of known immediate or delayed hypersensitivity reactions attributed to compounds of similar chemical or biologic composition to INCB039110, dabrafenib, or trametinib, or excipients or to dimethyl sulfoxide (DMSO). * Uncontrolled intercurrent illness including, but not limited to, ongoing or active serious infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, uncontrolled diabetes, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study because INCB039110, dabrafenib, and trametinib may have teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with the study drugs, breastfeeding should be discontinued prior to the mother being treated with the study drugs. * History of interstitial lung disease or pneumonitis. * Patients known to be HIV-positive patients and on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with the study drugs. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * History of another malignancy other than the study indication under this trial within 5 years of study enrollment. Does not apply to subjects who underwent successful definitive resection of basal or squamous cell carcinoma of the skin, superficial bladder cancer, in situ cervical cancer, in situ breast cancer, or other in situ cancers. * History or current evidence/risk of retinal vein occlusion (RVO) or retinal pigment epithelial detachment (RPED): * History of RVO or RPED, or predisposing factors to RVO or RPED (e.g., uncontrolled glaucoma or ocular hypertension, uncontrolled systemic disease such as hypertension, diabetes mellitus, or history of hyperviscosity or hypercoagulability syndromes). * Visible retinal pathology as assessed by ophthalmic exam that is considered a risk factor for RVO or RPED such as evidence of new optic disc cupping, evidence of new visual field defects, and intraocular pressure \>21 mm Hg. * History or evidence of cardiovascular risk including any of the following: * A QT interval corrected for heart rate using the Bazett's formula QTcB ≥460 msec on the pre-study baseline single 12 lead EKG. * History or evidence of current clinically significant uncontrolled arrhythmias (exception: patients with controlled atrial fibrillation for \>30 days prior to registration are eligible). * History of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to registration. * History or evidence of current ≥ Class II congestive heart failure as defined by the New York Heart Association (NYHA) functional classification system * Treatment-refractory hypertension defined as a blood pressure of systolic \>140 mmHg and/or diastolic \>90 mmHg which cannot be controlled by anti-hypertensive therapy. In patients with no history of hypertension and a pre-study baseline blood pressure of systolic \>140 mmHg and/or diastolic \>90 mmHg, a second reading should be taken at least 1 minute later, with the two readings averaged to obtain a final BP measurement. * 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. * Prior placement of an implantable defibrillator * History of or identification on screening imaging of intracardiac metastases * No known active infection with Hepatitis B Virus (HBV), or Hepatitis C Virus (HCV). Patients with chronic or cleared HBV infection and HCV infection are eligible. * For patients requiring anti-coagulation with vitamin K antagonists, therapeutic level dosing of warfarin can be used with close monitoring of PT/INR by the site. Exposure may be decreased due to enzyme induction when on treatment, thus warfarin dosing may need to be adjusted based upon PT/INR. Consequently, when discontinuing dabrafenib, warfarin exposure may be increased and thus close monitoring via PT/INR and warfarin dose adjustments must be made as clinically appropriate. If clinically indicated, prophylactic low dose warfarin may be given to maintain central catheter patency. * Current use of a prohibited medication. The following medications or non-drug therapies are prohibited * Other anti-cancer therapy while on study treatment. (note: megestrol \[Megace\] if used as an appetite stimulant is allowed). * Concurrent treatment with bisphosphonates is permitted; however, treatment must be initiated prior to the first dose of study therapy. Prophylactic use of bisphosphonates in patients without bone disease is not permitted, except for the treatment of osteoporosis. * Because the composition, PK, and metabolism of many herbal supplements are unknown, the concurrent use of all herbal supplements is prohibited during the study (including, but not limited to, St. John's wort, kava, ephedra \[ma huang\], ginkgo biloba, dehydroepiandrosterone \[DHEA\], yohimbe, saw palmetto, or ginseng). * Patients receiving any medications or substances that are strong inhibitors or inducers of CYP3A or CYP2C8 are ineligible. Current use of, or intended ongoing treatment with: herbal remedies (e.g., St. John's wort), or strong inhibitors or inducers of P-glycoprotein (Pgp) or breast cancer resistance protein 1 (Bcrp1) should also be excluded