Heated Intraperitoneal Chemotherapy and Gastrectomy for Gastric Cancer With Positive Peritoneal Cytology

Background: \- Gastric cancer is a common and serious cancer. Standard treatment is chemotherapy drugs. Researchers want to see if a new treatment helps. It is surgical removal of the cancer and heated chemotherapy delivered to the abdominal cavity called Hyperthermic intraperitoneal chemotherapy (HIPEC). Objective: \- To test if surgical removal of tumors plus heated intraperitoneal chemotherapy can improve survival in people with gastric cancers. Eligibility: \- People ages 18 and older with gastric cancer who can have most tumors surgically removed Design: * Participants will be screened with: * Medical history * Physical exam * Blood, urine, and heart tests * Scans * Tissue sample from previous surgery * Endoscopy with biopsy: A tube with a camera goes through the mouth and into the stomach. It and takes a sample of stomach tissue. Participants may get medicine to make them drowsy. * Laparoscopy: Small cuts are made in the abdomen. A thin tube with a light and camera is inserted into the abdomen. Participants sleep through the procedure. Participants will stay in the hospital. They will have: * Surgery to remove as many tumors as possible. * HIPEC for 60 minutes: Two thin tubes are put into the abdomen. Two chemotherapy drugs are given through one tube. They are drained out through another at a temperature a few degrees above normal body temperature. Another drug is given in a vein. * Recovery for 7-21 days: Participants will have tubes in their stomach and bladder and intravenous (IVs) for a few days. They will get pain medicine, IV fluids, antibiotics, and blood transfusions as needed. * Participants will have visits every few months for 3 years, then one a year. Visits include physical exam, blood tests, and scans. They also include dietary assessment and questions.