Surgery and Chemotherapy With or Without Chemotherapy After Surgery in Treating Patients With Ovarian, Fallopian Tube, Uterine, or Peritoneal Cancer

Inclusion Criteria: * Provided informed consent * Patient with primary or recurrent International Federation of Gynecology and Obstetrics (FIGO) stage III or IV, or recurrent ovarian, fallopian tube, peritoneal carcinoma, or uterine cancer, confined to abdominal cavity, including those who have completed neoadjuvant chemotherapy and primary surgery * Gynecologic Oncology Group (GOG) or Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 or Karnofsky scale (KPS) \>= 70% * Patients who are platinum-sensitive or platinum resistant * Candidate for potentially radical, maximal effort cytoreductive surgery at the discretion and expertise of the treating physician * For patients with newly diagnosed-ovarian/tubal/peritoneal cancer who have received pre-operative neoadjuvant chemotherapy, evidence of response must be documented by at least one of the following: * Decline in serum cancer antigen (CA) 125 level * At least a 30% decrease in the sum of the longest diameter of target lesions on radiographic imaging * Improvement of ascites volume * Neoadjuvant chemotherapy must be held for at least 3 weeks prior to surgery * Resolution of any effects of prior therapy (except alopecia and peripheral neuropathy) to the current National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (NCI CTCAE) grade =\< 1 and to baseline laboratory values as defined * Hemoglobin (HGB) \>= 9 g/dL * White blood cell (WBC) \>= 3,000/mcL * Absolute neutrophil co…