Nivolumab With or Without Ipilimumab in Treating Patients With Recurrent or High Grade Gynecologic Cancer With Metastatic Peritoneal Carcinomatosis

Inclusion Criteria: * Patients must have biopsy-confirmed ovarian or other gynecologic cancers (fallopian tube, peritoneal, endometrial, or cervical cancer) who have recurred after or progressed on frontline and one or more second-line standard treatments; patients with ovarian/fallopian tube/peritoneal cancers must have platinum refractory or resistant disease (defined as progression on a platinum containing regimen or recurrence within 180 days of prior dose of platinum-containing regimen), but do not require second-line treatment to be eligible for the dose-finding phase; eligibility for the expansion cohort will be limited to subjects with high grade epithelial ovarian, fallopian tube, or peritoneal carcinomas who have recurred after or progressed on frontline and one or more second-line standard treatments or have developed platinum resistant disease after frontline therapy (in which case progression on a second line therapy will not be required); however, for the dose expansion phase, potential subjects are not required to have platinum refractory or resistant disease * Measurable metastatic disease (by RECIST version \[v\] 1.1) in the peritoneal cavity or retroperitoneal lymph nodes; disease outside of the peritoneal cavity is allowed as long as metastatic sites are also present within the peritoneum/retroperitoneum * Absolute neutrophil count \>= 1500/mL * Platelets \>= 100,000/mL * Hemoglobin \>= 9 g/dL (transfusion to meet this criterion is allowed) * Serum creatinine clearance (CL) \>= 40 mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine collection for determination of creatinine clearance * Total bilirubin =\< 1.5 X upper limit of normal (ULN) * Aspartate aminotransferase (AST/serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT/serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN (=\< 5 X ULN in subjects with bone or liver metastases) * Eastern Cooperative Oncology Group (ECOG) performance status (PS) of 0 or 1 * Subjects must be \>= 4 weeks beyond treatment with any chemotherapy or other investigational therapy to include hormonal, biological, or targeted agents (\>= 8 weeks from previous bevacizumab treatment) at the time of first dose of study drug(s) * Women of child-bearing potential MUST have a negative serum human chorionic gonadotropin (HCG) test unless prior hysterectomy or menopause (defined as 12 consecutive months of amenorrhea); subjects are considered not to be of child-bearing potential if they are surgically sterilized or post-menopausal (\>= 50 years of age and has not had menses for greater than 1 year or with serum follicle stimulating hormone \[FSH\] in the menopausal range will be considered postmenopausal); subjects should not become pregnant or breastfeed while on this study; sexually active subjects of child bearing potential must agree to use contraception for the duration of study participation and for 5 months after the last dose of ipilimumab or nivolumab * Ability to understand and willingness to sign informed consent form prior to initiation of the study and any study procedures * Subjects in expansion cohort only: Willing to undergo pre- and on-treatment biopsies Exclusion Criteria: * Patients who are pregnant or breastfeeding * Patients with low grade ovarian/fallopian tube/peritoneal cancers * Prior immune checkpoint inhibitor therapy * History of inflammatory bowel disease (including ulcerative colitis and Crohn's disease), or any other known autoimmune diseases including rheumatoid arthritis, scleroderma, systemic lupus erythematosus, and autoimmune vasculitis * History of previous malignancy that in the principal investigator (PI)'s opinion has a reasonable chance of recurrence during the study period or otherwise confounding this clinical trial * Active peritonitis or diverticulitis * Patients requiring corticosteroids use at doses greater than prednisone 10 mg daily equivalent (use of inhaled steroids, and short-term steroid for radiologic contrast allergy, or treatment of immune-related adverse events are allowed) * Medical or surgical history that in the treating physician's opinion would make the subject not a suitable candidate for i.p. therapy; examples would include surgically documented extensive intraperitoneal adhesions or large volume ascites * History of chronic obstructive pulmonary disease (COPD) or other chronic pulmonary disease requiring systemic steroid therapy, oxygen, or hospitalization * Chronic hepatitis B or C virus infection, or known human immunodeficiency virus (HIV) positive, that might affect host immunity * Any other illness or condition that in the investigator's opinion would adversely affect the safety of checkpoint inhibitor therapy * Active infection requiring intravenous (IV) antibiotics or other uncontrolled intercurrent illness requiring hospitalization * Inability to comply with the study and follow-up procedures * History of cerebrovascular accident, myocardial infarction or unstable angina within the previous 6 months before starting therapy * Prolongation of QT interval (QT)/corrected QT interval (QTc) (QTc interval \> 470 ms) using the Fridericia method of QTc analysis * Known active central nervous system metastases and/or carcinomatous meningitis * History of severe hypersensitivity reaction with biologics therapy (monoclonal antibodies)