Inclusion Criteria:

          -  Female subject eligible to participate if she is not pregnant and at least one of the
             following conditions applies:

               -  Not a woman of child-bearing potential (WOCBP) OR

               -  WOCBP who agrees to follow the contraceptive guidance throughout the treatment
                  period and for at least 6 months after the final study drug administration

          -  Female subject must agree not to breastfeed starting at screening and throughout the
             study period, and for 6 months after the final study drug administration.

          -  Female subject must agree not to donate ova starting at screening and throughout the
             study period, and for 6 months after the final study drug administration.

          -  A sexually active male subject with a female partner(s) who is of child-bearing
             potential must agree to use contraception during the treatment period and for at least
             6 months after the final study drug administration.

          -  Male subject must agree not to donate sperm starting at screening and throughout the
             study period, and for 6 months after the final study drug administration.

          -  Male subject with a pregnant or breastfeeding partner(s) must agree to remain
             abstinent or use a condom for the duration of the pregnancy or time partner is
             breastfeeding throughout the study period and for 6 months after the final study drug
             administration.

          -  Subject has histologically confirmed gastric or GEJ adenocarcinoma.

          -  Subject has radiographically-confirmed, locally advanced, unresectable or metastatic
             disease within 28 days prior to the first dose of study treatment.

          -  Subject's tumor is positive for CLDN18.2 expression.

          -  Subject agrees to not participate in another interventional study while on treatment.

          -  Subject has ECOG performance status 0 to 1.

          -  Subject has predicted life expectancy ≥ 12 weeks.

          -  Subject must meet all of the following criteria based on the centrally or locally
             analyzed laboratory tests collected within 14 days prior to the first dose of study
             treatment. In case of multiple central laboratory data within this period, the most
             recent data should be used.

               -  Hemoglobin (Hgb) ≥ 9 g/dL (transfusion is allowed, but post-transfusion Hgb [24
                  hours or later following transfusion] must be ≥ 9 g/dL)

               -  Absolute neutrophil count (ANC) ≥ 1.5 × 109/L

               -  Platelets ≥ 100 × 10^9/L

               -  Albumin ≥ 2.5 g/dL

               -  Total bilirubin ≤ 1.5 × upper limit of normal (ULN)

               -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 × ULN
                  in subjects without liver metastases (≤ 5 × ULN if liver metastases are present)

               -  Estimated creatinine clearance ≥ 30 mL/min

               -  Prothrombin time/international normalized ratio and partial thromboplastin time ≤
                  1.5 × ULN (except for subjects receiving anticoagulation therapy)

        Specific to Cohort 1A:

          -  Subject has measurable disease according to RECIST 1.1 within 28 days prior to the
             first dose of study treatment per investigator assessment. For subjects with only 1
             evaluable lesion and prior radiotherapy ≤ 3 months before enrollment, the lesion must
             either be outside the field of prior radiotherapy or must have documented progression
             following radiation therapy.

          -  Subject has disease progression on or after at least 2 prior regimens for their
             advanced disease, including fluoropyrimidine and platinum-containing chemotherapy, and
             if appropriate, HER2/neu-targeted therapy.

          -  Subject must have an additional available tumor specimen collected within 3 months
             prior to the first dose of study treatment.

          -  Subject must be an appropriate candidate for a tumor biopsy and is amenable to undergo
             a tumor biopsy during the screening period (if applicable) and treatment period as
             indicated in the Schedule of Assessments.

        Specific to Cohort 2:

          -  Subject has measurable disease according to RECIST 1.1 within 28 days prior to the
             first dose of study treatment per investigator assessment. For subjects with only 1
             evaluable lesion and prior radiotherapy ≤ 3 months before enrollment, the lesion must
             either be outside the field of prior radiotherapy or must have documented progression
             following radiation therapy.

          -  Subject has not received prior systemic anti-cancer therapy for their advanced disease
             (subject may have received neoadjuvant and/or fluorouracil-containing adjuvant
             chemotherapy as long as it has been completed ≥ 6 months before the first dose of
             study treatment).

          -  Subject has a gastric or GEJ tumor that is HER2-negative as determined by local or
             central testing.

          -  Subject must have an additional available tumor specimen collected within 3 months
             prior to the first dose of study treatment.

          -  Subject must be an appropriate candidate for a tumor biopsy and is amenable to undergo
             a tumor biopsy during the screening period (if applicable) and treatment period as
             indicated in the Schedule of Assessments.

        Specific to Cohort 3A:

          -  Subject has radiologically evaluable disease (measurable and/or non-measurable)
             according to RECIST 1.1, per local assessment, ≤ 28 days prior to the first dose of
             study treatment. For subjects with only 1 evaluable lesion and prior radiotherapy ≤ 3
             months before enrollment, the lesion must either be outside the field of prior
             radiotherapy or must have documented progression following radiation therapy.

          -  Subject has disease progression on or after at least 2 prior regimens for their
             advanced disease, including fluoropyrimidine and platinum-containing chemotherapy, and
             if appropriate, HER2/neu-targeted therapy.

          -  Subject has not received prior checkpoint inhibitor therapy.

        Specific to Cohort 4A and 4B:

          -  Subject has radiologically evaluable disease.

          -  Subject has not received prior systemic anti-cancer therapy for their advanced
             disease.

          -  Subject has a gastric or GEJ tumor that is HER2-negative as determined by local or
             central testing.

          -  Subject has not received prior checkpoint inhibitor therapy.

        Specific to Cohort 4B Only:

          -  Subject must have an additional available tumor specimen collected within 3 months
             prior to the first dose of study treatment.

          -  Subject must be an appropriate candidate for a tumor biopsy and is amenable to undergo
             a tumor biopsy during the screening period (if applicable) and treatment period.

          -  Subject has a tumor that is PD-L1 positive.

        Exclusion Criteria:

          -  Subject has had prior severe allergic reaction or intolerance to known ingredients of
             zolbetuximab or other monoclonal antibodies, including humanized or chimeric
             antibodies.

          -  Subject has known immediate or delayed hypersensitivity or contraindication to any
             component of study treatment.

          -  Subject has received other investigational agents or devices concurrently or within 28
             days prior to first dose of study treatment.

          -  Subject has received systemic immunosuppressive therapy, including systemic
             corticosteroids 14 days prior to first dose of study treatment.

          -  Subject has a complete gastric outlet syndrome or a partial gastric outlet syndrome
             with persistent recurrent vomiting.

          -  Subject has significant gastric bleeding and/or untreated gastric ulcers that would
             preclude the subject from participation.

          -  Subject has history of central nervous system metastases and/or carcinomatous
             meningitis from gastric/GEJ cancer.

          -  Subject has a known history of a positive test for human immunodeficiency virus (HIV)
             infection or known active hepatitis B (positive hepatitis B surface antigen [HBsAg])
             or hepatitis C infection.

          -  Subject has had within 6 months prior to first dose of study treatment any of the
             following: unstable angina, myocardial infarction, ventricular arrhythmia requiring
             intervention or hospitalization for heart failure.

          -  Subject has active infection requiring systemic therapy that has not completely
             resolved within 7 days prior to the start of study treatment.

          -  Subject has active autoimmune disease that has required systemic treatment within the
             past 3 months prior to the start of study treatment.

          -  Subject has a clinically significant disease or co-morbidity that may adversely affect
             the safe delivery of treatment within this study or make the subject unsuitable for
             study participation.

          -  Subject has psychiatric illness or social situations that would preclude study
             compliance.

          -  Subject has had a major surgical procedure ≤ 28 days before start of study treatment.

          -  Subject is without complete recovery from a major surgical procedure ≤ 14 days before
             start of study treatment

               -  Subject has received radiotherapy for locally advanced unresectable or metastatic
                  gastric or GEJ adenocarcinoma ≤ 14 days (Cohorts 1 and 3A) and ≤ 28 days (Cohorts
                  2 and 4A or 4B) prior to start of study treatment and has NOT recovered from any
                  related toxicity.

               -  Subject has another malignancy, for which treatment is required.

          -  Cohort 2 and 4 Only, subject has any of the following:

               -  Prior severe allergic reaction or intolerance to any component of mFOLFOX6
                  chemotherapeutics in this study

               -  Known dihydropyrimidine dehydrogenase deficiency (DPD).

               -  Known peripheral neuropathy > Grade 1 (absence of deep tendon reflexes as the
                  sole neurological abnormality does not render the subject ineligible).

               -  Sinusoidal obstruction syndrome, formerly known as veno-occlusive disease, if
                  present, should be stable or improving.

               -  History of clinically significant ventricular arrhythmias.

               -  QTc interval > 450 msec for male subjects; QTc interval > 470 msec for female
                  subjects.

               -  History or family history of congenital long QT syndrome.

               -  Cardiac arrhythmias requiring anti-arrhythmic medications (Subjects with rate
                  controlled atrial fibrillation for > 1 month prior to first dose of study
                  treatment are eligible).

          -  Cohorts 3A, 4A and 4B Only, subject has any of the following:

               -  Subjects with ongoing or previous autoimmune disease or interstitial lung
                  disease, active diverticulitis or gastrointestinal ulcerative disease, or other
                  uncontrolled or clinically significant medical disorders.

               -  Subjects with type 1 diabetes mellitus, endocrinopathies stably maintained on
                  appropriate replacement therapy or skin disorders (e.g., vitiligo, psoriasis, or
                  alopecia) not requiring systemic treatment are allowed.

               -  Subject has known history of serious hypersensitivity reaction to a known
                  ingredient of pembrolizumab or nivolumab.

          -  Cohort 4B Only: Subject with known microsatellite instability-high or mismatch repair
             deficient tumors.