As Project Managers become more senior, what are the typical career paths (beyond just taking on larger and more complex projects)?
All the way up to COO
As your experience with larger/higher-budget/more-complex projects grows, you'll eventually be in a position to manage projects which directly affect the business in all areas, e.g. rolling out company-wide strategic initiatives. With enough experience in this, there's no reason you couldn't be invited to help decide on the initiatives in the first place.