This is a two part study. Part 1 will test increasing dose levels of ASP9853 in combination with docetaxel. Part 2 will test increasing doses of ASP9853 combined with paclitaxel. Each part will determine the maximum tolerated dose and recommended Phase 2 dose for ASP9853 in combination with each taxane. Preliminary evidence of antitumor activity of ASP9853 in combination with docetaxel or with paclitaxel also will be explored.