A Phase 1/1b Study of ASP2138 in Participants with Metastatic or Locally Advanced Unresectable Gastric or Gastroesophageal Junction (GEJ) Adenocarcinoma or Metastatic Pancreatic Adenocarcinoma Whose Tumors Have Claudin (CLDN) 18.2 Expression

Inclusion Criteria: - Participant is considered an adult according to local regulation at the time of signing the informed consent form (ICF). - Female participant is not pregnant, confirmed by serum pregnancy test and medical evaluation by interview and at least 1 of the following conditions apply: - Not a woman of childbearing potential (WOCBP) - WOCBP who agrees to follow the contraceptive guidance from the time of informed consent through at least 6 months after final study intervention administration. - Female participant must agree not to breastfeed starting at screening and throughout the study period and for 6 months after the final study intervention administration. - Female participant must not donate ova starting at screening and throughout the study period and for 6 months after the final study intervention administration. - Male participant with female partner(s) of childbearing potential (including breastfeeding partner) must agree to use contraception throughout the treatment period and for 6 months after the final study intervention administration. - Male participant must not donate sperm during the treatment period and for 6 months after the final study intervention administration. - Male participant with 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 intervention administration. - Participant's tumor sample is positive for claudin (CLDN)18.2 expression by central immunohistochemistry (IHC) testing. - Participant has radiographically-confirmed, locally advanced, unresectable or metastatic disease within 28 days prior to the first dose of study intervention. - Participant has at least 1 measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 within 28 days prior to the first dose of study intervention. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. - Participant has QT interval by Fredericia (QTcF) =< 470 msec. - Participant agrees not to participate in another interventional study while receiving study Intervention in the present study. - Participant has Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. - Participant has predicted life expectancy >= 12 weeks. - Participant must meet all of criteria based on laboratory tests within 7 days prior to the first dose of study Intervention. In case of multiple laboratory data within this period, the most recent data should be used. If a participant has received a recent blood transfusion, the laboratory tests must be obtained >= 2 weeks after any blood transfusion. Monotherapy Disease specific Criteria: Gastric/GEJ Cancer - Participant has histologically confirmed gastric/gastroesophageal junction (GEJ) adenocarcinoma. - Escalation: Participant with gastric/GEJ adenocarcinoma who has progressed, is intolerant, has refused, or for whom there is no standard approved therapies that impart significant clinical benefit (no limit to the number of prior treatment regimens). - Unique to South Korea: Participant with gastric/GEJ adenocarcinoma who has refused standard approved therapies is not allowed. - Expansion: Participant with gastric/GEJ adenocarcinoma must have received no more than 3 prior lines of systemic chemotherapy treatment. Monotherapy Disease specific Criteria: Pancreatic Cancer - Participant has histologically or cytologically confirmed pancreatic adenocarcinoma. - Escalation: Participant with pancreatic adenocarcinoma who has progressed, is intolerant, has refused, or for whom there is no standard approved therapies that impart significant clinical benefit (no limit to the number of prior treatment regimens). - Unique to South Korea: Participant with pancreatic adenocarcinoma who has refused standard approved therapies is not allowed. - Expansion: Participants with pancreatic adenocarcinoma must have received no more than 2 prior lines of systemic chemotherapy treatment. For all participants in combination therapy administration: - If a participant has received a recent blood transfusion, the laboratory tests must be obtained ≥ 1 week after any blood transfusion. Combination Therapy Disease specific Criteria: ASP2138 in Combination with Pembrolizumab and mFOLFOX6 as First-line Therapy in Gastric/GEJ Cancer - Participant has histologically confirmed diagnosis of gastric/GEJ adenocarcinoma. - Participant has metastatic or locally advanced unresectable gastric/GEJ adenocarcinoma. - Participant with gastric/GEJ adenocarcinoma has progressed and must not have been previously treated for metastatic disease with either chemotherapy or prior checkpoint inhibitor therapy. - Participant has a human epidermal growth factor receptor 2 (HER2)-negative tumor per local testing. Combination Therapy Disease Specific Criteria: ASP2138 in Combination with Ramucirumab and Paclitaxel as Second-line Therapy in Gastric/GEJ Cancer - Participant has histologically confirmed diagnosis of gastric/GEJ adenocarcinoma. - Participant has metastatic or locally advanced unresectable gastric/GEJ adenocarcinoma. - Participant with gastric/GEJ adenocarcinoma must have previously received 1 line of systemic chemotherapy treatment (i.e., documented objective radiological or clinical disease progression during or within 4 months of the last dose of first line platinum and fluoropyrimidine doublet or disease progression during or after perioperative fluorouracil, leucovorin, oxaliplatin and docetaxel [FLOT]). Combination Therapy Disease specific Criteria: ASP2138 in Combination with mFOLFIRINOX as First-line Therapy in Pancreatic Cancer - Participant has histologically or cytologically confirmed diagnosis of pancreatic adenocarcinoma. - Participant has confirmed metastatic or locally advanced unresectable pancreatic adenocarcinoma. - Participant has pancreatic adenocarcinoma, has progressed and must not have received prior systemic anticancer therapy for their advanced disease. Exclusion Criteria: - Participant has received other investigational agents, or antineoplastic therapy including other immunotherapy or devices concurrently or within 21 days or 5 times the half-life, whichever is shorter, prior to first dose of study intervention administration. - Participant has any condition which makes the participant unsuitable for study participation. - Participant has known immediate or delayed hypersensitivity or contraindication to any component of study intervention. - Participant has had prior severe allergic reaction or intolerance to known ingredients of ASP2138 or other antibodies, including humanized or chimeric antibodies. - Participant weighs < 40 kg. - Participant has received systemic immunosuppressive therapy, including systemic corticosteroids 14 days prior to first dose of study intervention. Participant using a physiologic replacement dose of hydrocortisone or its equivalent (defined as up to 30 mg per day of hydrocortisone or up to 10 mg per day of prednisone), receiving a single daily dose of systemic corticosteroids or receiving systemic corticosteroids as pre-medication for radiologic imaging contrast use are allowed. - Participant has a complete gastric outlet syndrome or a partial gastric outlet syndrome with persistent/recurrent vomiting. - Participant has significant gastric bleeding and/or untreated gastric ulcers that exclude the participant from participation. - Participant has symptomatic CNS metastases or participant has evidence of unstable CNS metastases even if asymptomatic (e.g., progression on scans). Participants with previously treated CNS metastases are eligible, if they are clinically stable and have no evidence of CNS progression by imaging for at least 4 weeks prior to start of study intervention and are not requiring immunosuppressive doses of systemic steroids (> 30 mg per day of hydrocortisone or > 10 mg per day of prednisone or equivalent) for longer than 2 weeks. - Participant is known to have HIV infection. However, participants with cluster of differentiation (CD4) + T cell counts >= 350 cells/µL and no history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infections within the past 6 months are eligible. NOTE: Screening for human immunodeficiency virus (HIV) infection should be conducted per local requirements. - Participant is known to have active hepatitis B (positive hepatitis B surface antigen [HBsAg]) or hepatitis C infection. Testing is required for known history of these infections or as mandated by local requirements. NOTE: Screening for these infections should be conducted per local requirements. - For participant who is negative for HBsAg, but hepatitis B core antibody (HBc Ab) positive, a hepatitis B virus (HBV) deoxyribonucleic acid (DNA) test will be performed and if positive the participant will be excluded. - Participant with positive hepatitis C virus (HCV) serology, but negative HCV ribonucleic acid (RNA) test results are eligible. - Participant treated for HCV with undetectable viral load results are eligible - Participant has had within 6 months prior to first dose of study intervention any of the following: unstable angina, myocardial infarction, ventricular arrhythmia requiring intervention or hospitalization for heart failure. - Participant has active infection requiring systemic therapy that has not completely resolved within 7 days prior to the start of study intervention. - Participant has active autoimmune disease that has required systemic immunosuppressive treatment within the past 1 month prior to the start of study intervention. - Participant has a clinically significant disease or co-morbidity that may adversely affect the safe delivery of treatment within this study or make the participant unsuitable for study participation. - Participant has psychiatric illness or social situations that would preclude study compliance. - Participant has had a major surgical procedure 28 days before start of study intervention and has not fully recovered. - Participant has received radiotherapy metastatic or for locally advanced unresectable gastric/GEJ or metastatic pancreatic adenocarcinoma 14 days prior to start of study intervention and has NOT recovered from any related toxicity. - Participant has another malignancy for which treatment is required. - Participant who has received CLDN18.2-targeted therapy (e.g., zolbetuximab or chimeric antigen receptor CLDN18.2-specific T cells) prior to first dose of study intervention administration is not eligible for dose escalation cohorts. However, a participant who has received CLDN18.2-targeted therapy greater than 28 days or 5 half-lives (whichever is longer) prior to first dose study intervention administration is eligible for dose expansion cohorts only, with the exception of participants who have experienced Grade >= 3 gastrointestinal toxicity after receiving an CLDN18.2-targeted therapy. - Participant has a history or complication of interstitial lung disease. China Specific: Participant who has received treatment with herbal medications that have known antitumor activity within 28 days prior to first dose of study treatment. For all participants in combination therapy administration: - Participant has prior severe allergic reaction; suspected, known immediate or delayed hypersensitivity; or intolerance or contraindication to any study intervention (i.e., pembrolizumab and mFOLFOX6 [all components], ramucirumab and paclitaxel or mFOLFIRINOX [all components]). - For 5 FU (fluorouracil): Participant has known dihydropyrimidine dehydrogenase (DPD) deficiency. (NOTE: Screening for DPD deficiency should be conducted per local requirements). - Participants who have received systemic immunosuppressive therapy, including systemic corticosteroids 14 days prior to the first dose of study intervention are generally excluded; however, participants using a physiologic replacement dose of hydrocortisone or its equivalent (defined as up to 30 mg per day of hydrocortisone or up to 10 mg per day of prednisone), receiving a single daily dose of systemic corticosteroids or receiving systemic corticosteroids as pre-medication for radiologic imaging contrast or for chemotherapy (as part of combination therapy administration) are allowed. - Participant is known to have HIV infection. - NOTE: Differing from monotherapy administration, participants with CD4+ T cell counts ≥ 350 cells/µL and no history of AIDS-defining opportunistic infections within the past 6 months remain ineligible. - NOTE: Screening for HIV infection should be conducted per local requirements. - Participant has had uncontrolled high blood pressure within 6 months prior to the first dose of study intervention. - Participant has a history of ascites requiring drainage more than twice in the past 7 days.