NAUTILUS: OKI-179 Plus Binimetinib in Patients with Advanced Solid Tumors in the RAS Pathway (Phase 1b) and NRAS-mutated Melanoma (Phase 2)

Inclusion Criteria: * Phase 1b: Solid tumor refractory to standard treatment, for which no standard therapy is available, or if the patient refuses standard therapy * Phase 1b: Tumor has an activating mutation in the RAS pathway confirmed by any local or central laboratory, including but not limited to RAS, BRAF, NF1, and GNAQ/11 * Phase 1b: Prior MEK inhibitor exposure may be allowed per Sponsor agreement * Phase 2: Histologically confirmed, metastatic melanoma with a confirmed NRAS mutation determined by a validated NRAS mutation detection kit performed in a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory * Phase 2: Prior ICI treatment with a programmed cell death 1 (PD-1) or programmed death ligand 1 (PD-L1) checkpoint inhibitor, or ineligible for this type of therapy * Phase 2: Consent for a tumor biopsy or can provide a recent archival tumor biopsy sample (within 2 years) * Phase 2: At least 1 measurable lesion based on RECIST version 1.1 * Eastern Cooperative Oncology Group performance status of 0 or 1 * Normal organ and marrow function as defined below: * Absolute neutrophil count ≥ 1.5 × 109/L * Platelets ≥ 100,000/μL * Hemoglobin ≥ 9.0 g/dL (at least 1 week after packed red blood cells, if applicable) * Total bilirubin within institutional ULN, unless patient has Gilbert's syndrome and has total bilirubin ≤ 2.5 × institutional ULN * Alanine aminotransferase and aspartate aminotransferase ≤ 2.5 × institutional ULN or \< 5 × institutional ULN in the presence of liver metastasis * Serum creatinine \< 1.5 × institutional ULN * All prior treatment-related toxicities must have resolved to CTCAE version 5.0 criteria of Grade ≤ 1, except for alopecia and ICI-related endocrinopathies managed with hormone replacement therapy (eg, thyroiditis/hypothyroidism, hypophysitis, diabetes mellitus type 1) * Left ventricular ejection fraction (LVEF) ≥ 50% * Able to swallow and tolerate oral medications * Life expectancy ≥ 3 months Exclusion Criteria: * Any of the prior treatments, as described below: * Major surgery within 28 days of C1D1 * Chemotherapy or radiation within 2 weeks of C1D1 * Investigational agents within 4 weeks of C1D1 or \< 5 half-lives, whichever is shorter, or expected toxicity not resolved to CTCAE version 5.0 criteria of Grade ≤ 1, except for alopecia and ICI-related endocrinopathies managed with hormone replacement therapy * Prior histone deacetylases inhibitors, MEK inhibitors (Phase 2 only), pan-deacetylating agents, or valproic acid for the treatment of cancer * Untreated or symptomatic brain metastasis. Patients with previously treated brain metastasis who are not on corticosteroids and are clinically stable are eligible for enrollment, as are patients with small (\< 0.5 cm) untreated and asymptomatic brain metastases * Known hypersensitivity to binimetinib or other MEK inhibitors * Women who are pregnant or nursing * Concomitant active malignancies or previous malignancies with \< 2-year disease-free interval at the time of enrollment. Patients with adequately resected basal or squamous cell carcinoma of the skin, carcinoma in situ of the cervix or breast, stage 1 prostate cancer, or other malignancies deemed to be cured by prior therapy in the judgment of the Investigator may enroll irrespective of the time of diagnosis * Any severe concurrent medical or psychiatric condition (including active systemic infection requiring intravenous antibiotics, uncontrolled diabetes mellitus, symptomatic congestive heart failure, uncontrolled hypertension, or cardiac arrhythmia) which, in the judgment of the Investigator, would make the patient inappropriate for study participation * Impaired cardiovascular function or clinically significant cardiovascular diseases, including any of the following: * History of acute myocardial infarction, acute coronary syndromes (including unstable angina, coronary artery bypass graft, coronary angioplasty or stenting) \< 6 months prior to start of study treatment * Symptomatic congestive heart failure (Grade 2 or higher), history or current evidence of clinically significant cardiac arrhythmia and/or conduction abnormality \< 6 months prior to the start of study treatment, except medically managed atrial fibrillation or paroxysmal supraventricular tachycardia * Uncontrolled arterial hypertension despite medical management * History or evidence of central serous retinopathy (CSR), retinal vein occlusion (RVO) or any eye condition that would be considered a risk factor for CSR or RVO, such as uncontrolled glaucoma or ocular hypertension * Known previous or current serious ophthalmic disease, history of cataract surgery within \< 8 days, serious eye trauma, or intraocular or ocular surgery other than refractive surgery (i.e. LASIK, cataract); patients with uveal melanoma/eye enucleation due to uveal melanoma are permitted to enroll * Patients who have neuromuscular disorders that are associated with elevated creatine phosphokinase (CPK; eg, inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy) or elevated baseline CPK levels (≥ Grade 2) * History of recent (≤ 90 days) thromboembolic or cerebrovascular event such as transient ischemic attack, cerebrovascular accident, or hemodynamically significant (massive or submassive) deep vein thrombosis or pulmonary emboli (DVT/PE). Note: Patients with DVT/PE that does not result in hemodynamic instability may enroll as long as they are anticoagulated for at least 4 weeks. Note: Patients with DVT/PE related to indwelling catheters or other procedures may enroll * Any medical condition that would impair the administration of oral agents, such as active inflammatory bowel disease or uncontrolled nausea, vomiting, or diarrhea * Known positive serology for HIV and AIDS-related illness with CD4 count \< 350/mL and/or known active hepatitis B or hepatitis C. Testing prior to C1D1 is not required * History or current evidence of congenital long QT syndrome * QTcF corrected with Fridericia's formula \> 470 msec on screening electrocardiogram (ECG) * Ongoing medication that leads to significant QT prolongation * Ongoing medication that is a strong cytochrome P450 3A4 inhibitor or inducer * Ongoing medication that is a strong inhibitor of P-glycoprotein and sensitive substrates