M6620 (VX-970) in Selected Solid Tumors

This study is made up of two phases: a Translational Lead-In Phase and a Phase II. These two phases serve different functions. The translational lead-in phase is designed to test the drug on a small number of patients in efforts to gain information on two research questions: * If M6620 has an anti-cancer effect on participants * If M6620 research findings that were discovered in laboratory studies are also found in human research studies. Phase II is a much larger study to determine if M6620 has an anti-cancer effect in different groups of patients. The FDA (the U.S. Food and Drug Administration) has not approved M6620 as a treatment for any disease. ATR is an enzyme in cells that is responsible for multiple functions including repairing damaged DNA, helping cells that are stressed during the DNA copying process, and working to maintain the ends of chromosomes. In cancer cells, active ATR enzymes protect the cancer by helping the cells repair damage, stay alive, and maintain health. M6620 is a drug designed to inhibit the ATR enzyme. Inhibiting ATR may block how cancers repair their naturally damaged DNA, handle cancer cell stress, and maintain cancer cell life and health. Administration of M6620 may therefore assist in the slowing of growth or destruction of some cancers. In this research study, the investigators are... * Gathering initial data on the anti-cancer activity of M6620 when given alone to participants within selected cancer populations * Determining if there are changes in the biological components in the participant's body that may be associated with damaged DNA repair