It's been done in a variety of other Westminster-model countries, using several different models - a lot of former UK colonies moved away from the Queen as head

It's been done in a variety of other Westminster-model countries, using several different models - a lot of former UK colonies moved away from the Queen as head of state on independence. The closest eqivalent in kind is probably Ireland, where the President is also mostly a figurehead who holds reserve powers. Some countries have moved further to systems with an executive President, though.