Spoilers for the March 16 episode of General Hospital indicate that Peter is going to push hard in his quest to convince Maxie to stay with him. He showed up at her apartment during Monday's show and all signs point toward some tense exchanges on Tuesday.
Last week, Anna confronted Peter. It was an intense conversation that left her with a lot of regret and heartbreak. Soon after that, Peter showed up at Maxie's place, anxious to talk to her once more.