A Study of Prexasertib (LY2606368) With Chemotherapy or Targeted Agents in Participants With Advanced Cancer

The primary purpose of Parts A, B, C, D and E of this study is to determine a recommended dose level and schedule of prexasertib (an inhibitor of checkpoint kinase 1 and 2 \[CHK1/CHK2\] in combination with: * cisplatin (Part A) * cetuximab (Part B) * pemetrexed (Part C) * fluorouracil (Part D) * LY3023414 (Part E) \[An inhibitor of phosphoinositide 3-kinase alpha (PI3K alpha) and mammalian target of rapamycin (mTOR), DNA-dependent protein kinase (DNA-PK), and other class I phosphoinositide 3-kinase (PI3K) family members\] in participants with advanced or metastatic cancer. Part A dose expansion of the study will evaluate the safety and toxicity of prexasertib at the recommended dose level in combination with cisplatin in participants with advanced or metastatic cancer, Part B dose expansion of the study will evaluate the safety and toxicity of prexasertib at the recommended dose level in combination with cetuximab in participants with advanced or metastatic colorectal cancer, Part C and D dose expansions have been removed and Part E dose expansion of the study will evaluate the safety and toxicity of prexasertib at the recommended dose level in combination with LY3023414 in participants with advanced or metastatic cancer, participants with PIK3CA mutations, or with advanced or metastatic breast cancer. In Parts A and B the effect of adding granulocyte colony stimulating factor (G-CSF) to cisplatin in combination with prexasertib and cetuximab in combination with prexasertib will be explored. In Part A the effect of changing the schedule of prexasertib and cisplatin also will be explored. In Part B the effect of changing the schedule of prexasertib and cetuximab also will be explored.