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

* 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 \<= 30 (out of 39 possible points)
* Age \>= 18 years.
* ECOG performance status \<= 1 (Karnofsky \>= 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 \<=1.5x institutional upper limit of normal (ULN)
  * AST (SGOT)/ ALT (SGPT) \<= 3x institutional upper limit of normal (ULN), or \<= 5.0x ULN in participants with liver metastases (only)
  * Creatinine within normal institutional limits

OR

--Creatinine clearance \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal calculated using eGFR.

* Because therapeutic agents used in this trial are known to be teratogenic, individuals of child-bearing potential (IOCBP) and individuals who are able to father a child must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for 180 days after last study treatment.
* Ability of participant to understand and the willingness to sign a written informed consent document.
* Ability and willingness of the participant to co-enroll on the tissue collection protocol 13C0176, Tumor, Normal Tissue and Specimens from Patients Undergoing Evaluation or Surgical Resection of Solid Tumors .

EXCLUSION CRITERIA:

* Participants with known extra-abdominal metastatic disease from the participant s appendiceal, colorectal, ovarian, or peritoneal mesothelioma primary.
* Participants who have received intraperitoneal chemotherapy or other anti-cancer therapy within the last 4 weeks prior to the start of study treatment.
* Participants who have undergone major surgery within the last 12 weeks prior to the start of study treatment.
* History of allergic reactions attributed to platinum-containing compounds.
* History of dihydropyrimidine dehydrogenase deficiency (only participants with appendiceal or colorectal cancer).
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
* Pregnant individuals are excluded from this study because the protocol involves major abdominal surgery and chemotherapeutic agents with the potential for teratogenic or abortifacient effects. Note: Due to an unknown but potential risk for adverse events in nursing infants secondary to treatment of the participant, nursing (including breastfeeding) should be discontinued if the participant is undergoing treatment (i.e., nursing participants must agree to discontinue nursing activities).
* HIV-positive participants with detectable viral load despite antiretroviral therapy are ineligible because of participants increased risk of lethal infections when treated with marrow-suppressive therapy. HIV-positive participants who have undetectable viral load on antiretroviral therapy may be considered for this study only after consultation with a NIAID physician.