This is a wank where everyone does well!
And I don't want the third system to merely be somewhere on number line between capitalism and socialism, say 70% capitalism and 30% socialism and getting regulation about right. No, I want it to be something really different.
For example, I've heard of Gandhian economics and feminist economics. I've heard of parecom which is an abbreviation for participatory economics.
Maybe an approach based on a particular indigenous world view and ethic which is a dynamic system with plenty of quick-cycle feedback?