Ph II Study of Cabozantinib With Pembrolizumab in Metastatic Gastric and Gastroesophageal Adenocarcinoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed gastric or gastroesophageal adenocarcinoma * Must have locally advanced, recurrent, or metastatic disease not amenable to curative intent surgery. * Must have progressed, or not tolerated, at least one line of treatment with a platinum and/or fluoropyrimidine containing regimen. At least one cycle of combination chemotherapy including a platinum (oxaliplatin, cisplatin, carboplatin) and/or fluoropyrimidine (capecitabine or 5-Fluorouracil) based regimen for advanced disease. Combination regimens with platinum/fluoropyrimidine containing a taxane and or a checkpoint inhibitor are allowed. Patients progressing within six months of perioperative chemotherapy or definitive chemoradiation for localized disease are eligible. Patients who have exhausted all other standard of care options are also eligible. * Must have received and progressed on one previous line of treatment containing a checkpoint inhibitor (if PD-L1 Combined Positive Score (CPS) score unknown or ≥ 10%). Patients with PD-L1 CPS score \< 10% are eligible independent of whether they have received previous checkpoint inhibitors. * Age ≥ 18 years * Performance status: Eastern Cooperative Oncology Group (ECOG) performance status ≤2 * Life expectancy of greater than 3 months * Adequate organ and marrow function as defined below: 1. Leukocytes: ≥ 2,000/mcL 2. absolute neutrophil count: ≥ 1000/mcL 3. platelets: ≥ 60,000/mcl 4. total bilirubin: within normal institutional limits (or \<3mg/dL in patients with Gilbert's disease) 5. AST(SGOT)/ALT(SPGT): ≤ 3 X institutional upper limit of normal or ≤ 5 X if liver metastases are present 6. creatinine: \< 1.5 X upper limit of normal 7. hemoglobin: ≥ 8 g/dL 8. Serum albumin: ≥ 2.8 g/dL 9. Urine protein/creatinine ration (UPCR): ≤ 1 mg/mg * The effects of cabozantinib on the developing human fetus at the recommended therapeutic dose are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 4 months following completion of therapy. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * A female of child-bearing potential is any woman (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria: 1. Has not undergone a hysterectomy or bilateral oophorectomy; or 2. Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months). * Ability to swallow tablets * Ability to understand and the willingness to sign a written informed consent. * Patients with known MSI-High or dMMR tumors must have disease progression after at least one line of immunotherapy Exclusion Criteria: * Patients who have had chemotherapy within 2 weeks prior to entering the study * All toxicities attributed to prior anti-cancer therapy other than alopecia must have resolved to grade 1 or baseline * Patients may not be receiving any other investigational agents. * Patients with known brain metastases or cranial epidural disease unless accurately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks before first dose of study treatment. These individuals should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. Eligible subjects must be neurologically asymptomatic and without corticosteroid treatment at the time of the first dose of study treatment. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to pembrolizumab, cabozantinib or other agents used in study. Patients with documented previous immune related toxicities which led to discontinuation of a checkpoint inhibitor. * Concomitant anticoagulation with oral anticoagulants (eg, warfarin), direct thrombin inhibitors (e.g., dabigatran), direct factor Xa inhibitors betrixaban, or platelet inhibitors (eg, clopidogrel). Allowed anticoagulants are the following: 1. Prophylactic use of low-dose aspirin for cardio-protection (per local applicable guidelines) and low-dose low molecular weight heparins (LMWH). 2. Therapeutic doses of LMWH or anticoagulation with direct factor Xa inhibitors rivaroxaban, or apixaban in subjects without known brain metastases who are on a stable dose of the anticoagulant for at least 1 week before first dose of study treatment without clinically significant hemorrhagic complications from the anticoagulation regimen or the tumor. * The subject has prothrombin time (PT)/INR or partial thromboplastin time (PTT) test ≥ 1.3 x the laboratory ULN within 7 days before the first dose of study treatment. * Uncontrolled intercurrent illness including, but not limited to, the following conditions: 1. ongoing or active infection 2. symptomatic congestive heart failure 3. uncontrolled hypertension defined as sustained blood pressure (BP) \> 150 mm Hg systolic or \> 100 mm Hg diastolic despite optimal antihypertensive treatment 4. Stroke (including transient ischemic attack \[TIA\]), myocardial infarction (MI), or other ischemic event, or thromboembolic event (eg, deep venous thrombosis, pulmonary embolism) within 6 months before first dose 5. unstable angina pectoris 6. cardiac arrhythmia 7. evidence of tumor invading GI tract, active peptic ulcer disease, inflammatory inflammatory bowel disease (eg, Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, acute pancreatitis, acute obstruction of the pancreatic duct or common bile duct, or gastric outlet obstruction. 8. Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose. 9. Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose. 10. Clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5 ml) of red blood, or other history of significant bleeding (eg, pulmonary hemorrhage) within 12 weeks before first dose. 11. Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation. 12. Lesions invading any major blood vessels. 13. Other clinically significant disorders that would preclude safe study participation: 1. Serious non-healing wound/ulcer/bone fracture 2. Uncompensated/symptomatic hypothyroidism 3. Moderate to severe hepatic impairment (Child-Pugh B or C) 14. psychiatric illness/social situations that would limit compliance with study requirements. * Major surgery (e.g., laparoscopic nephrectomy, GI surgery, removal or biopsy of brain metastasis) within 2 weeks before first dose of study treatment. Minor surgeries within 10 days before first dose. Subjects must have complete wound healing from major surgery or minor surgery before first dose of study treatment. Subjects with clinically relevant ongoing complications from prior surgery are not eligible. * Prior treatment with cabozantinib * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 ms per electrocardiogram (ECG) within 28 days before first dose of study treatment. 1. Corrected QT (QTc) = QT / ∛RR 1. QT: duration of QT interval 2. RR: duration of RR interval 2. Note: If a single ECG shows a QTcF with an absolute value \> 500 ms, two additional ECGs at intervals of approximately 3 min must be performed within 30 min after the initial ECG, and the average of these three consecutive results for QTcF will be used to determine eligibility. * Receipt of any type of small molecule kinase inhibitor (including investigational kinase inhibitor) within 2 weeks before first dose of study treatment. * History of another primary cancer within the last 3 years with the exception of non-melanoma skin cancer, early-stage prostate cancer, or curatively treated cervical carcinoma in-situ and not treated with systemic therapy. * Inability to comply with study and follow-up procedures as judged by the Investigator * Patients must not be pregnant or nursing due to the potential for congenital abnormalities and the potential of this regimen to harm nursing infants. * Has squamous cell or undifferentiated gastric cancer. * Has received prior cytotoxic, biologic or other systemic anticancer therapy including investigational agents within 2 weeks prior to randomization. * Radiation therapy for bone metastasis within 2 weeks, any other radiation therapy within 4 weeks before first dose of study treatment. Systemic treatment with radionuclides within 6 weeks before the first dose of study treatment. Subjects with clinically relevant ongoing complications from prior radiation therapy are not eligible. * Has received a live vaccine within 30 days prior to the first dose of study intervention. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study intervention. * Has severe hypersensitivity (Grade ≥ 3) to pembrolizumab or cabozantinib and/or any of their excipients. * Has an active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease-modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Has an active infection requiring systemic therapy. * Has a known history of human immunodeficiency virus (HIV) infection. 1\. Note: No HIV testing is required unless mandated by local health authority. * Has a known history of active tuberculosis (TB; Bacillus tuberculosis). * Has a history or current evidence of any condition (eg, known deficiency of the enzyme dihydropyrimidine dehydrogenase), therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating investigator.