The purpose of this study is to find a recommended schedule and dose range for LY2875358 when given with ramucirumab that may be safely given to participants with cancer. In Part A of this study, escalating doses of LY2875358 will be given in combination with a fixed dose of ramucirumab to evaluate the safety of the combination. After a recommended schedule and dose range of LY2875358 and ramucirumab has been established, Part B of the study will confirm safety and to see how well certain tumors respond to the combination of study drugs. The average amount of time on study is expected to be about 6 months.