Can a government work where both the Prime Minister and the President have equal power instead of one clearly being above the other?

I’ve seen systems where one role is mostly symbolic and the other runs the government, but I’m curious about a setup where both positions genuinely share authority equally. Would that create better balance and accountability, or would it just lead to constant deadlock and rivalry?

Are there any real-world examples that came close to this, and do you think it could work long term?