Birinapant and Carboplatin in Treating Patients and Targeting Recurrent High Grade Ovarian, Fallopian Tube, or Primary Peritoneal Cancer (HGSOC)

PRIMARY OBJECTIVES: I. To assess whether addition of birinapant to carboplatin therapy can reduce the percentage of platinum resistant tumor initiating cells by 50% compared to pre-therapy biopsies in participants with recurrent high grade serous ovarian carcinomas (HGSOC) whose tumors score positive in the in vitro organoid bioassay test. II. Assess target engagement by comparing levels of cellular inhibitor of apoptosis protein (cIAP) and percentage of apoptotic cells in pre-versus post therapy tumor biopsies (obtained after three cycles of treatment). SECONDARY OBJECTIVES: I. To see if there is an increase in progression free survival of participants treated with co-therapy (birinapant/carboplatin) compared with historic controls. TERTIARY OBJECTIVES: I. Develop a companion diagnostic test by correlating clinical response seen in participants with two biomarker assays developed in our laboratory. 1. Measuring levels of cIAP protein by western blot in tumor biopsies obtained from participants prior to start of therapy. 2. Measuring percentage of cIAP positive cells by immunohistochemistry in tumor biopsies obtained from participants prior to start of therapy. OUTLINE: Patients receive birinapant intravenously (IV) over 30 minutes on days 1 and 8, and carboplatin IV over 30 minutes to 1 hour on day 1. Treatment repeats every 21 days for up to 6 courses in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months for up to 2 years from Course 1, Day 1.