A Study of ASP2138 Given by Itself or Given With Other Cancer Treatments in Adults With Stomach Cancer, Gastroesophageal Junction Cancer, or Pancreatic Cancer

Claudin 18.2 protein, or CLDN18.2 is a protein found on cells in the digestive system. It is also found on some tumors. Researchers are looking at ways to attack CLDN18.2 to help control tumors. ASP2138 is thought to bind to CLDN18.2 and a protein on a type of immune cell called a T-cell. This "tells" the immune system to attack the tumor. ASP2138 is a potential treatment for people with stomach cancer, gastroesophageal junction cancer (GEJ cancer) or pancreatic cancer. GEJ is where the tube that carries food (esophagus) joins the stomach. Before ASP2138 is available as a treatment, the researchers need to understand how it is processed by and acts upon the body. In this study, ASP2138 will either be given by itself, or given together with standard treatments for gastric, GEJ and pancreatic cancer. Pembrolizumab and mFOLFOX6, and ramucirumab and paclitaxel are standard treatments for gastric and GEJ cancer. mFOLFIRINOX is a standard treatment for pancreatic cancer. This information will help find a suitable dose of ASP2138 given by itself and together with the standard cancer treatments and to check for potential medical problems from the treatments. The main aims of the study are: * To check the safety of ASP2138 and how well people can tolerate medical problems during the study. * To find a suitable dose of ASP2138 to be used later in the study. * These are done for ASP2138 given by itself and when given together with the standard cancer treatments. Adults 18 years or older with stomach cancer, GEJ cancer, or pancreatic cancer can take part. Their cancer is locally advanced unresectable or metastatic. Locally advanced means the cancer has spread to nearby tissue. Unresectable means the cancer cannot be removed by surgery. Metastatic means the cancer has spread to other parts of the body. There should also be the CLDN18.2 marker in a tumor sample. People cannot take part if they need to take medicines to suppress their immune system, have blockages or bleeding in their gut, have specific uncontrollable cancers, have specific infections, have a condition such as hemophagocytic lymphohistiocytosis (HLH) which is when the body over-reacts to a "trigger" such as infection, or have a specific heart condition ("New York Heart Association Class III or IV"). Phase 1: Lower to higher doses of ASP2138 * ASP2138 is either given through a vein (intravenous infusion) or just under the skin (subcutaneous injection). * Different small groups are given lower to higher doses of ASAP2138. * ASP2138 is either given by itself, or given with 1 of 3 standard treatments: * Pembrolizumab and mFOLFOX6 (first treatment for gastric GEJ cancer) * Ramacirumab and paclitaxel (Second treatment for gastric or GEJ cancer) * ASP2138 with mFOLFIRINOX (first treatment for pancreatic cancer) Phase 1b: doses of ASP2138 worked out from Phase 1 * ASP2138 is either given through a vein or just under the skin. This depends on the findings from Phase 1. * People with gastric cancer, GEJ cancer or pancreatic cancer are given doses of ASP2138, worked out from Phase 1. * This includes doses of ASP2138 given by itself and ASP2138 given with the standard cancer treatments. * The standard cancer treatments given depends on the type of cancer they have. End of treatment visit: This is 7 days after final dose of study treatment or if the study doctor decides to stop the person's treatment. People who have locally advanced unresectable pancreatic cancer will not receive ASP2138 by itself.