Hyperthermic Intraperitoneal Chemotherapy With Cisplatin During Surgery or Cisplatin Before Surgery for the Treatment of Stage III or IV Ovarian, Fallopian Tube or Peritoneal Cancer

PRIMARY OBJECTIVES: I. To evaluate the safety and tolerability of intravenous (IV) cisplatin on the day prior to interval cytoreductive surgery (CRS) to administration of hyperthermic intraepithelial chemotherapy (HIPEC) with cisplatin at the completion of interval cytoreductive surgery. SECONDARY OBJECTIVES: I. Feasibility of each of the treatment options. II. Treatment delays. III. Perioperative outcomes. IV. Quality of life/patient reported outcomes. V. Recurrence free survival (RFS) and overall survival (OS). VI. Changes to the gut MIcrobiome OUTLINE: Patients receive carboplatin IV and paclitaxel IV on day 1. Treatment repeats every 3 weeks for 3-4 cycles in the absence of disease progression or unacceptable toxicity. Within 3-4 weeks following the third or fourth neoadjuvant cycle, patients who achieve complete or partial response undergo interval debulking surgery Patients are randomized to 1 of 2 arms. ARM I: Patients receive cisplatin IV the day prior to interval cytoreductive surgery ARM II: Patients undergo HIPEC and receive cisplatin IV over 90 minutes at the time of interval cytoreductive surgery All patients undergo stool sample collection and diagnostic imaging throughout the trial. After completion of study treatment, patients are followed up for up to 30 days.