The primary objective of this study is to evaluate the safety and tolerability of ONO-7746 across multiple doses in patients with solid tumors and chemotherapy induced thrombocytopenia (CIT) scheduled to receive at least two cycles of myelosuppressive chemotherapy on Day 1 every 21 days at the same dosages and schedule in the study. The secondary objectives are to characterize the PK profiles of ONO-7746 and to explore the pharmacodynamic effect of ONO-7746 on CIT.