Do it like India.
Elect the President, as head of state, separately from [insert title here], as Head of Government - if you don't have the Houses of Congress choose the head of government as a Prime Minister or General Secretary or what have you.
The real advantage is that because the Head of State has limited duties, it doesn't break anything if they have to be fired for whatever reason, and that the Head of Government is in theory just a regular person with a government job, so there is reason not to apply regular laws to them so you skip over any requirements for immunity.
Elect the President, as head of state, separately from [insert title here], as Head of Government - if you don't have the Houses of Congress choose the head of government as a Prime Minister or General Secretary or what have you.
The real advantage is that because the Head of State has limited duties, it doesn't break anything if they have to be fired for whatever reason, and that the Head of Government is in theory just a regular person with a government job, so there is reason not to apply regular laws to them so you skip over any requirements for immunity.
-Now available with copious trivia!