This is a Phase 1b/2, open-label, multicenter study of DSP-7888 Dosing Emulsion in combination with checkpoint inhibitors (nivolumab or pembrolizumab) in adult patients with solid tumors, that consists of 2 parts: dose search part of the study (Phase 1b and Phase 1b Enrichment Cohort) and the dose expansion part of the study (Phase 2). In Phase 1b of this study there will be 2 arms: Arm 1 and Arm 2. In Arm 1, there will be 6 to 12 patients who will be dosed with DSP-7888 Dosing Emulsion and nivolumab and in Arm 2 there will be 6 to 12 patients who will be dosed with DSP-7888 Dosing Emulsion and pembrolizumab. In addition, an enrichment cohort of a further 10 patients who have locally advanced or metastatic Renal Cell Carcinoma or Urothelial Cancer with primary or acquired resistance to previous checkpoint inhibitors will be enrolled into Phase 1b of the study to help evaluate the preliminary antitumor activity of DSP-7888 Dosing Emulsion at the safe dose level identified in the dose-search part of the study, and will be dosed with DSP-7888 Dosing Emulsion and nivolumab, or DSP-7888 Dosing Emulsion and pembrolizumab, as per the investigator's preference. At the safe, recommended dose determined in Phase 1b, platinum-resistant ovarian cancer (PROC) patients will be enrolled in Phase 2 of the study with DSP-7888 Dosing Emulsion, exploring the combination with pembrolizumab (Arm 2). In Phase 2, approximately 40 patients with PROC will be initially enrolled; additional patients may be enrolled to further assess anti-tumor activities, but the total sample size will not exceed 60 patients. This brings the total maximum study population to approximately 84 patients.