In that case, we need a collective Presidency.
To exercise the powers that, as we have somehow managed to convince ourselves, the whole point of the Queen is that she does not actually exercise, even though she has them. I know.
The seat-taking members of the House of Commons could elect seven, the number in Switzerland, by each voting for one candidate from outside Parliament, with the seven highest-scorers elected for the duration of that Parliament. Ties for seventh place could be settled by a division of the whole House.
Four of them would then have to approve any exercise of the Royal Prerogative, including the granting of Royal Assent to any legislation, with the approval of all seven required for military action.
Or the seat-takings MPs from each of England, Scotland, Wales and Northern Ireland could elect one, of whom the one for England would have four votes, the one for Scotland three votes, the one for Wales two votes, and the one for Northern Ireland one vote.
It would take six of those 10 votes in order to approve any exercise of the Royal Prerogative, including the granting of Royal Assent to any legislation, with all 10 required for military action.
The monarchy would of course continue to exist for ceremonial purposes. As at present.