This trial proposes to evaluate the immunologic and potential clinical effectiveness of intensive locoregional sequential intraperitoneal (IP) cisplatin (IPC) with intravenous (iv) paclitaxel followed by peritoneal infusion of a chemokine modulatory (CKM) regimen composed of a cocktail of IP rintatolimod and interferon-alpha (IFNα) for patients with advanced stage ovarian cancer (III-IV) in the primary neoadjuvant setting. It was previously determined the tolerable dose of IPC-CKM. This study will add intradermal (ID) autologous αDC1 vaccines (known to be nontoxic) to the tolerable IPC-CKM regimen and systemic Keytruda (pembrolizumab). To optimize the pattern of immunity, all patients will also receive oral celecoxib (COX2 inhibitor).