Ruxolitinib Phosphate, Paclitaxel, and Carboplatin in Treating Patients With Stage III-IV Epithelial Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Patients must have clinically and radiographically suspected and previously untreated International Federation of Gynecologic and Obstetrics (FIGO) stage III or IV epithelial ovarian, primary peritoneal or fallopian tube cancer, high grade, for whom the plan of management will include neoadjuvant chemotherapy (NACT) with interval tumor reductive surgery (TRS) who have undergone biopsies for histologic confirmation * Institutional confirmation of Mullerian epithelial adenocarcinoma on core biopsy (not cytology or fine needle aspiration) or laparoscopic biopsy; (for phase II of the study formalin-fixed paraffin-embedded \[FFPE\] tissue should be available for laboratory analysis); patients with the following histologic epithelial cell types are eligible: high grade serous carcinoma, high grade endometrioid carcinoma, clear cell carcinoma, or a combination of these * All patients must have measurable disease as defined by Response Evaluation Criteria In Solid Tumors (RECIST) 1.1; measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI) or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Appropriate stage for study entry based on the following diagnostic workup: …