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.