Open-label Phase 1b Study of Ulixertinib and Cetuximab or Ulixertinib in Combination With Cetuximab and Encorafenib in Patients With Unresectable or Metastatic Colorectal Cancer Who Have Previously Received EGFR or BRAF-directed Therapy

Inclusion Criteria: Patients must meet all of the inclusion criteria to be eligible: 1. Provision of signed Informed Consent prior to any screening procedures being performed. 1. Non-English speaking patients will be eligible for participation with involvement of the MD Anderson Language Assistance department in the informed consent process (per MD Anderson SOP 04\_Informed Consent Process). 2. Individuals lacking the ability, based on reasonable medical judgment, to understand and appreciate the nature and consequences of participation in this study will not be eligible for participation. 2. Age ≥ 18 years at the time of informed consent. 3. Histologically (or cytologically) confirmed diagnosis of adenocarcinoma of the colon or rectum, with clinical confirmation of unresectable and/or metastatic disease that is measurable according to RECIST1.1 criteria. 4. Mutation status at the time of colorectal cancer diagnosis performed on tumor tissue or circulating tumor DNA (prior to any systemic chemotherapy): 1. Cohort A: KRAS, NRAS, EGFR ectodomain, BRAF V600E wild-type status 2. BRAF expansion Cohort: BRAF V600E mutation must be present 5. Prior treatment with at least one systemic chemotherapy regimen for mCRC, or recurrence/progression with development of unresectable or metastatic disease within 6 months of adjuvant chemotherapy for resected colorectal cancer. 6. Prior treatment with: a. Cohort A: anti-EGFR therapy (cetuximab or panitumumab) setting for at least 16 weeks with either CR or PR as best response, prior to progression b. BRAF expansion Cohort: BRAF therapy (not including regorafenib) and anti-EGFR therapy (cetuximab or panitumumab) 7. ECOG performance status ≤ 1. 8. Patients who received chemotherapy must have recovered (Common Terminology Criteria for Adverse Events \[CTCAE\] Grade ≤1) from the acute effects of chemotherapy except for residual alopecia or Grade 2 peripheral neuropathy prior to day 1 of study. A washout period of at least 21 days is required between last chemotherapy dose and day 1 of study (provided the patient did not receive radiotherapy). 9. Patients who received radiotherapy must have completed and fully recovered from the acute effects of radiotherapy. A washout period of at least 7 days is required between end of radiotherapy and day 1 of study. 10. Adequate hematologic status: Absolute neutrophil count (ANC) ≥ 1.5 x 109/L; Hemoglobin (Hgb) ≥ 9 g/dL with or without transfusions; Platelets (PLT) ≥ 100 x 109/L without transfusions 11. Adequate liver function: 1. ALT and AST ≤3 × ULN, or ≤5 × ULN in the presence of liver metastases 2. Total bilirubin ≤ 1.5 × ULN i. Note: Patients who have a total bilirubin level \> 1.5 x ULN will be allowed if their indirect bilirubin level is ≤ 1.5 x ULN. ii. Note: Participants with hyperbilirubinemia due to non-hepatic cause (eg, hemolysis, hematoma) may be enrolled following discussion and agreement with the principle investigator. 12. Adequate renal function: either serum creatinine ≤ 1.5 x ULN, or calculated creatinine clearance (determined as per Cockcroft-Gault) ≥ 50mL/min at screening are acceptable. 13. QTc interval ≤ 480 ms (preferably the mean from triplicate ECGs) 14. Able to take oral medications. 15. Because the teratogenicity of cetuximab is not known, the patient, if sexually active, must be postmenopausal, surgically sterile, or using effective contraception (hormonal or barrier methods). Female patients of childbearing potential must have a negative serum pregnancy test within 7 days prior to enrollment 16. Willing and able to participate in the trial and comply with all trial requirements. 17. Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational agent may be included after consultation with the Principle Investigator. Exclusion Criteria: Patients who fulfill one or more of the following criteria will not be eligible for inclusion in this trial: 1. History of grade 3 or 4 allergic reaction or intolerability attributed to cetuximab or panitumumab. 2. History of allergic reactions attributed to compounds of chemical or biologic composition similar to those of cetuximab, or if the patient had red meat allergy/tick bite history. 3. History of a Grade 3 or 4 allergic reaction or intolerability attributed to encorafenib or other BRAF inhibitor (BRAF Expansion Cohort) <!-- --> 1. Previously exposed to ERK1/2 inhibitor 2. Any known symptomatic brain metastasis • Note: Patients previously treated or untreated for this condition who are asymptomatic in the absence of corticosteroid and anti-epileptic therapy are allowed. Known brain metastases must be stable for ≥ 4 weeks, with imaging (e.g., magnetic resonance imaging \[MRI\] or computed tomography \[CT\]) demonstrating no current evidence of progressive brain metastases at screening. 3. Known leptomeningeal disease 4. A history or current evidence/risk of retinal vein occlusion (RVO) or central serous retinopathy (CSR). 5. Previous or concurrent malignancy within 3 years of study entry, with the following exceptions: adequately treated basal or squamous cell skin cancer, superficial bladder cancer, prostate intraepithelial neoplasm, carcinoma in-situ of the cervix, or other noninvasive or indolent malignancy; other solid tumors treated curatively without evidence of recurrence for at least 3 years prior to study entry. 6. Impaired cardiovascular function or clinically significant cardiovascular diseases, including any of the following: * History of acute coronary syndromes (including myocardial infarction, unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) \<12 months prior to screening, * Symptomatic chronic heart failure (i.e. NYHA class 3 or higher), history or current evidence of clinically significant cardiac arrhythmia and/or conduction abnormality \<6 months prior to screening except atrial fibrillation and paroxysmal supraventricular tachycardia, * The patient has a personal history of any of the following conditions: syncope of cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest. 7. Uncontrolled hypertension defined as persistent elevation of systolic blood pressure ≥ 170 mmHg or diastolic blood pressure ≥ 100 mm Hg, despite current therapy; 8. The patient has active systemic bacterial or fungal infection (requiring intravenous (IV) antibiotics and/or antifungals at time of initiating study treatment). 9. Participants positive for HIV are ineligible unless they meet all of the following: a. A stable regimen of HAART that is not contraindicated b. No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections c. A CD4 count \>250 cells/mcL, and an undetectable HIV viral load on standard PCR-based tests. 10. Active hepatitis B or hepatitis C infection a. Active HBV is defined as any of the following: • HBsAg(+), HBV DNA \>200 IU/mL (36 copies/mL); * HBsAg(+), HBV DNA ≤200 IU/mL and persistent or intermittent elevation of ALT/AST and/or liver biopsy showing chronic hepatitis with moderate or severe necroinflammation. * Note: Participants who are HBsAg(-), HBcAb(+) are eligible and should be monitored/treated as per local standard of care. b. Active HCV is defined as: * HCV antibody positive; AND * Presence of HCV RNA. 11. Impaired gastrointestinal function or disease that may significantly alter the absorption of study drug (e.g., ulcerative diseases, uncontrolled vomiting, malabsorption syndrome, small bowel resection with decreased intestinal absorption). 12. Any other condition that would, in the Investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures. 13. Major surgery ≤ 6 weeks prior to starting study drug or failure to recover from side effects of such procedure at the discretion of the treating investigator. 14. Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a female after conception and until the termination of gestation, confirmed by a positive hCG laboratory test. 15. Medical, psychiatric, cognitive or other conditions that may compromise the patient's ability to understand the patient information, give informed consent, comply with the study protocol or complete the study