Encorafenib, Cetuximab, and Nivolumab in Treating Patients With Microsatellite Stable, BRAFV600E Mutated Unresectable or Metastatic Colorectal Cancer

Inclusion Criteria: * Provision of signed Informed Consent prior to any screening procedures being performed. A translator may be used for patients who do not speak or read English. * Age ≥ 18 years at the time of informed consent. * 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. * Confirmation of BRAFV600E tumor as detected by a CLIA-certified laboratory. * Confirmation of MSS status in a CLIA-certified laboratory. * Cohort A only: Prior treatment with at least one, but no more than two, systemic chemotherapy regimen(s) for mCRC, or recurrence/progression with development of unresectable or metastatic disease within 6 months of adjuvant chemotherapy for resected colorectal cancer. * Cohort B only: prior treatment with a BRAF, anti-EGFR, MEK, or ERK targeted therapy for treatment of colorectal cancer * ECOG performance status \< 1 * Adequate bone marrow, organ function and laboratory parameters: * Absolute neutrophil count (ANC) ≥ 1.0 x 109/L, * Hemoglobin (Hgb) ≥ 9 g/dL with or without transfusions, * Platelets (PLT) ≥ 100 x 109/L without transfusions, * AST and/or ALT ≤ 2.5 × upper limit of normal (ULN). If liver metastases are present, then it is acceptable for AST level ≤ 5.0 × ULN, and an ALT level ≤ 5.0 × ULN. * Total bilirubin ≤ 1.5 × ULN and \< 2 mg/dL 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 * Serum Creatinine ≤ 1.5 x ULN, or calculated creatinine clearance (determined as per Cockcroft-Gault) ≥ 50mL/min at screening; * QTc interval ≤ 480 ms (preferably the mean from triplicate ECGs) ; * Able to take oral medications; * Female patients are either postmenopausal for at least 1 year, are surgically sterile for at least 6 weeks, or must agree to take appropriate precautions to avoid pregnancy from screening through follow-up if of childbearing potential Note: Permitted contraception methods listed in Section 8.2 should be communicated to the patients and their understanding confirmed. For all females, the pregnancy test result must be negative within 24 hours of starting treatment with nivolumab. Males must agree to take appropriate precautions to avoid fathering a child from screening through 100 days following the end of therapy. Exclusion Criteria: * Concurrent corticosteroid therapy or concurrent use of any other immunosuppressive medication (corticosteroid use on study as a pre-medication for IV contrast allergies/reactions is allowed). Subjects who are receiving daily steroid replacement therapy (the equivalent of prednisone ≤10 mg daily) serve as an exception to this rule. * Cohort A only: Prior treatment with a BRAF inhibitor, MEK inhibitor, or ERK inhibitor (of note, regorafenib is not considered a BRAF inhibitor for the context of eligibility criteria). * Cohort A only: Prior treatment with anti-EGFR therapies. * Prior immune checkpoint therapy including, but not limited to, an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody, or any other prior immune-modulating agent administered with antineoplastic intent (monoclonal antibodies used against VEGF are permitted).. * Prior allogeneic tissue/solid organ transplant. * History of (non-infectious) pneumonitis that has required oral or IV steroids. * Receipt of a live vaccine within 30 days prior to the first administration of study medication. Seasonal flu vaccines that do not contain a live virus are permitted. * History of a Grade 3 or 4 allergic reaction attributed to humanized or human monoclonal antibody therapy. * Cohort B only: unacceptable toxicity to prior BRAF, EGFR, MEK, or ERK inhibitor therapy that in the discretion of the evaluating physician deems the participant at risk of excessive toxicity * Active infection requiring concurrent antibiotic use. * Any 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. 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. * Leptomeningeal disease * 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. * 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) \<6 months prior to screening, * Symptomatic chronic heart failure (i.e. Grade 2 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; * Uncontrolled hypertension defined as persistent elevation of systolic blood pressure ≥ 170 mmHg or diastolic blood pressure ≥ 100 mm Hg, despite current therapy; * Known positive serology for HIV (Human immunodeficiency virus), active hepatitis B, and/or active hepatitis C infection; * Known history of acute or chronic pancreatitis (history of acute pancreatitis with no recurrent events in the prior 24 months are permitted) * Patients with a history of inflammatory bowel disease, including ulcerative colitis and Crohn's disease, are excluded from this study, as are patients with a history of symptomatic autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, autoimmune vasculitis \[e.g., Wegener's Granulomatosis\]); CNS or motor neuropathy considered of autoimmune origin (e.g., Guillain-Barre Syndrome and myasthenia gravis, multiple sclerosis). Patients with Graves' disease will be allowed. * 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) * 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. * 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. * 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 * Medical, psychiatric, cognitive or other conditions, according to clinician judgment, that may compromise the patient's ability to understand the patient information, give informed consent, comply with the study protocol or complete the study.