Inclusion Criteria:  Male or female patient aged ≥ 18 years. Histologically confirmed esophageal adenocarcinoma, esophageal squamous cell carcinoma, GEJ adenocarcinoma, gastric adenocarcinoma, pancreatic adenocarcinoma, intrahepatic cholangiocarcinoma, perihilar cholangiocarcinoma, extrahepatic cholangiocarcinoma, or colorectal adenocarcinoma harboring a MAPK-mutated GI malignancy: KRAS, NRAS, HRAS, BRAF non-V600, MEK 1/2 (MAP2K1/2), or ERK 1/2 (MAPK3/1).  Progression on or during standard lines of therapy:  Patients with intrahepatic cholangiocarcinoma, perihilar cholangiocarcinoma, or extrahepatic cholangiocarcinoma must have progressed during or after receiving a first-line regimen of gemcitabine/cisplatin unless deemed ineligible by the treating investigator to receive chemotherapy-based regimens due to prior comorbidities. Patients with pancreatic adenocarcinoma must have progressed during or after first-line therapy of FOLFIRINOX/ mFOLFIRINOX, gemcitabine/nab-paclitaxel unless deemed ineligible by the treating investigator to receive chemotherapy-based regimens due to prior comorbidities. Patients with colorectal adenocarcinoma must have progressed during or after their first two lines of therapy, including FOLFOX ± Avastin and FOLFIRI ± Avastin, unless deemed ineligible by the treating investigator to receive chemotherapy-based regimens due to prior comorbidities. Patients with esophageal adenocarcinoma, esophageal squamous cell carcinoma, GEJ adenocarcinoma, or gastric adenocarcinoma must have progressed during or after their first two lines of therapy. Acceptable first-line regimens: FOLFOX, 5-FU/Cisplatin, FOLFIRI, Paclitaxel/Cisplatin or Carboplatin, Docetaxel/Cisplatin, DCF (or modifications thereof), or ECF (or modifications thereof) unless deemed ineligible by the treating investigator to receive chemotherapy-based regimens due to prior comorbidities. Acceptable second-line regimens: Ramucirumab/Paclitaxel, Docetaxel, Paclitaxel, Irinotecan, Trifluridine/Tipiracil, or FOLFIRI, unless deemed ineligible by the treating investigator to receive chemotherapy-based regimens due to prior comorbidities. Patients with dMMR/MSI-H tumors must have progressed during or after pembrolizumab. Measurable disease by RECIST 1.1 criteria by CT or MRI. Willing to provide a biopsy at the time points indicated on the Schedule of Activities. ECOG Performance Status ≤ 1.  Adequate organ function as defined as:  Hematologic:  Absolute neutrophil count (ANC) ≥ 1500/mm3 Platelet count ≥ 100,000/mm3 Hemoglobin ≥ 9 g/dL  Hepatic:  Total Bilirubin ≤ 1.5x institutional upper limit of normal (ULN) AST(SGOT)/ALT(SGPT) ≤ 3 × institutional ULN Patients with liver metastases will be allowed to enroll with AST and ALT levels ≤ 5 x ULN.  Renal:  Estimated creatinine clearance ≥ 50 mL/min by Cockcroft-Gault formula:  Males:  (140-age) × weight [kg] / serum creatinine [mgdL] × 72  Females:  ((140-age) × weight [kg] / serum creatinine [mgdL] × 72)×0.85  For female patients: Negative serum pregnancy test within 72 hours prior to first dose of study drugs for women of childbearing potential. The following definitions apply:  Women of childbearing potential, defined as a sexually mature woman: Has not been naturally post-menopausal for at least 12 consecutive months (i.e., who has had menses anytime in the preceding 12 consecutive months). Has not undergone menopause, surgical sterilization (bilateral oophorectomy or hysterectomy). Underwent surgical sterilization (bilateral oophorectomy or hysterectomy). Women not of childbearing potential: Amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, if any. Underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy). Male and female patients of childbearing potential agree to use highly effective contraception throughout the study and at least 90 days after the last study treatment administration. Recovery to baseline or ≤ Grade 1 CTCAE v5.0 from toxicities related to any prior cancer therapy, unless considered clinically not significant by the treating investigator. Able to provide informed consent and willing to sign an approved consent form that conforms to federal and institutional guidelines.  Exclusion Criteria:  Received systemic antineoplastic therapy (including unconjugated therapeutic antibodies and toxin immunoconjugates) or any investigational therapy ≤ 14 days or within five half-lives prior to starting study treatment, whichever is shorter.  Received radiotherapy ≤ 14 days prior to the first dose of study treatment.  Note: Localized radiation therapy for the treatment of symptomatic bone metastasis is allowed during that timeframe.  Undergone major surgery ≤ 3 weeks prior to starting study drug or who have not fully recovered from major surgery. The diagnosis of another malignancy within ≤ 3 years before study enrollment, except for those considered to be adequately treated with no evidence of disease or symptoms and/or will not require therapy during the study duration (i.e., basal cell or squamous cell skin cancer, carcinoma in situ of the breast, bladder or of the cervix, or low-grade prostate cancer with Gleason Score ≤ 6).  Known uncontrolled brain metastases or cranial epidural disease.  Note: Patients with stable brain metastases either treated or being treated with a stable dose of steroids (<20 mg of prednisone daily or equivalent) or anticonvulsants, with no dose change within 4 weeks before the first study drug dose, and no anticipated dose change, are eligible. In the event of steroid taper post-radiation therapy, taper must be complete within 2 weeks before Baseline.  History or current evidence of central serous retinopathy (CSR) or retinal vein occlusion (RVO) or current risk factors for RVO (e.g. uncontrolled glaucoma or ocular hypertension, history of hyperviscosity).  Current evidence of uncontrolled, significant intercurrent illness including, but not limited to, the following conditions:  Cardiovascular disorders:  Congestive heart failure New York Heart Association Class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias. Stroke (including transient ischemic attack [TIA]), myocardial infarction (MI), or other ischemic events, or thromboembolic event (eg, deep venous thrombosis, pulmonary embolism) within 3 months before the first dose. QTc prolongation defined as a QTcF > 500 ms. Known congenital long QT. Left ventricular ejection fraction < 50%.  History of seizures  Impairment of gastrointestinal function or gastrointestinal disease (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, or malabsorption syndrome).  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 (e.g., infection/inflammation, intestinal obstruction, unable to swallow medication, [patients may not receive the drug through a feeding tube], social/ psychological issues, etc.)  Prior stomach or duodenal resection that in the opinion of the Principal Investigator and Medical Monitor would affect the breakdown and absorption of the study medications. A patient with a feeding tube should also be excluded, as ulixertinib capsules cannot be broken apart.  Known HIV infection with a detectable viral load within 6 months of the anticipated start of treatment.  Note: Patients on effective antiretroviral therapy with an undetectable viral load within 6 months of the anticipated start of treatment are eligible for this trial.  Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination, radiographic findings, and TB testing in line with local practice), hepatitis B (known positive HBV surface antigen (HBsAg) result), or hepatitis C.  Note: Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody [anti-HBc] and absence of HBsAg) are eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA.  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. Known prior severe hypersensitivity to investigational product (IP) or any component in its formulations (NCI CTCAE v5.0 Grade ≥ 3). Patients taking prohibited medications as described in protocol. A washout period of prohibited medications for a period of at least 5 half-lives or as clinically indicated should occur before the start of treatment.