Individual Response to Hyperthermic Intraperitoneal Chemotherapy (HIPEC) Treatment of Peritoneal Carcinomatosis From Peritoneal Mesothelioma or Atypical Mesothelial Proliferation or From Ovarian, Colorectal, or Appendiceal Histologies

Background: Cytoreductive surgery (CRS) removes tumors in the abdomen. HIPEC is hyperthermic (heated) chemotherapy that washes the inside of the abdomen. CRS with HIPEC may help people with peritoneal carcinomatosis. These are tumors that have spread to the lining of the abdomen from other cancers. Researchers think they can improve the results of CRS with HIPEC treatment on these tumors by choosing the chemotherapy drugs used in HIPEC. Objective: To see if HIPEC after CRS can be improved, using either a model called the SMART (Sustained Microenvironment for Analysis of Resected Tissue) System or using 3-D cell culture (organoid) models, in order to test different chemotherapy drugs on tumors that were surgically removed prior to HIPEC treatment (these models are not attached to the body) versus tumors that were treated with HIPEC while still inside the body before being immediately surgically removed. Eligibility: Adults ages 18 and older who have peritoneal carcinomatosis that cannot be fully removed safely with surgery. Design: Participants will be screened with: Medical history Physical exam Blood and urine tests Electrocardiogram (EKG) Computed tomography (CT) scan Other imaging scans, as needed Tumor biopsy, if needed Laparoscopy (small cuts are made in the abdomen, and a tube with a light and a camera is used to see the organs in the abdomen), if needed Participants will enroll in NIH protocol #13C0176. This allows their tumor samples to be used in future research. Some screening tests may be repeated in the study. Participants will have CRS. As many of their visible tumors will be removed as possible during surgery except for a few specific tumors left to receive the HIPEC treatment. Then they will receive HIPEC and the remaining tumors will be immediately removed. Participants will be in the hospital for 7-21 days after this surgery (CRS with HIPEC). Participants will give tumor, fluid samples (from the abdomen during surgery), blood, saliva, cheek swab, and stool for research. They will complete surveys about their health and quality of life. Participants with peritoneal mesothelioma (mesothelioma primary only) will have genetic (DNA) testing to determine clinical (CLIA level) germline BAP1 status for research use. Participants will have follow-up visits for up to 5 years from CRS with HIPEC. If there is disease progression, participants may have CRS with HIPEC again. Participants will then have follow-up visits for up to 5 years from the date of last CRS with HIPEC.

* INCLUSION CRITERIA: * Confirmation of peritoneal carcinomatosis from peritoneal mesothelioma or atypical mesothelial proliferation, or from appendiceal, colorectal, or ovarian, histologies by the Laboratory of Pathology, NCI. * Measurable or evaluable disease as defined by RECIST v1.1. criteria and/or by peritoneal carcinomatosis index (PCI) score. * Participants must be assessed to be able to undergo optimal cytoreduction (i.e., completeness of cytoreduction score of 1 or 0) with laparoscopically assessed PCI score threshold as indicated below: * Primary Histology: Appendiceal/Colorectal/Ovarian / PCI Cutoff for Eligibility: Total Score \< 20 (out of 39 possible points) * Primary Histology: Mesothelioma or atypical mesothelial proliferation / PCI Cutoff for Eligibility: Total Score \= 18 years. * ECOG performance status \= 80%). * Participants must have adequate organ and marrow function as defined below: * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 75,000/mcL * Total bilirubin within \