Selumetinib and Olaparib in Solid Tumors

This study has 2 phases: Phase 1 (dose escalation) and Phase 2 (dose expansion). The goal of Phase 1 of this clinical research study is to find the highest tolerable dose combination of selumetinib and olaparib that can be given to patients who have solid tumors that are advanced or recurrent (has returned after treatment). The goal of Phase 2 is to learn if the highest tolerable dose combination found in Phase 1 can help to control advanced or recurrent solid tumors. The safety of the study drug combination will also be studied in both parts. This is an investigational study. Selumetinib is not FDA approved or commercially available. It is currently being used for research purposes only. Olaparib is FDA approved and commercially available for the treatment of ovarian cancer that has a certain type of genetic mutation (change). It is considered investigational to use selumetinib in combination with olaparib to treat advanced or recurrent cancer. The study doctor can explain how the study drugs are designed to work. Up to 90 participants will be enrolled in this study. All will take part at MD Anderson.