When the people you're interviewing with are 'already senior' (e.g. direct reports to the CEO), you can sometimes make your case worse rather than better, because it feels like you're going over their head.

If that happens then it's a very good thing - you do not want to work at a company where people are precious about how they succeed. If a great candidate (e.g you) drops into the inbox of the CEO who forwards it to someone else, and their first reaction is 'Well, they violated my personal kingdom by going over my head!' then that is a manager you do not need in your life.