High-grade serous ovarian cancer (HGSOC) remains a major clinical challenge. In particular among those patients with homologous recombination (HR)-proficient tumors (>50%), most eventually succumb to their disease due to high recurrence rates, acquired resistance, and cumulative toxicity. This report summarizes work from the 12 IMO Workshop in which we explored an alternative "extinction therapy" strategy for frontline treatment of HGSOC. Inspired by ecological principles, this multi-strike approach aims to eradicate tumors not through a singular "magic bullet" but through a series of therapies after standard frontline treatment when the tumor is still, and perhaps most, vulnerable. We present a framework leveraging mathematical modeling (MM) to develop personalized multi-strike protocols for HGSOC. Key contributions include: 1) An "IMOme" score using liquid biopsy data to assess patient-specific hematopoietic toxicity risk, guiding the timing and selection of subsequent therapies, 2) MM strategies to design effective low-dose combinations of targeted agents to achieve synthetic lethality while managing toxicity, and 3) A MM framework to analyze the interplay between chemotherapy, gut microbiome toxicity, and immunotherapy, demonstrating how mitigating microbiome damage could enhance immune response. Overall, the computational approaches presented herein aim to support the design of personalized, multi-strike regimens in the frontline setting that proactively target tumor extinction while managing toxicity, ultimately seeking to deliver cures for patients with HGSOC.