The purpose of the study is to test the safety of the study drug, ASTX029, and to find the appropriate dose of this experimental drug to use in this and other studies. The drug that will be given to you in this study, ASTX029, is investigational. This means it has not been approved for treatment of any disease, including cancer. Are you Eligible? (Inclusion Criteria) Do you have an advanced solid tumor that is unresectable or metastatic? Is your tumor able to be biopsied? Have you not received an extracellular signal-reduced kinase (ERK) inhibitor?