What role a monarch in a 32 county Ireland?

Thanks to Boland’s Ghost for pointing us in the direction of Gay Mitchell’s latest kite flying exercise, when he asks if there would be a role for a monarch in a 32 county Republic. It is, as Boland notes, a role back from the position held by Collins in treaty negotiations, since the Irish Republican project has never had more than a derisory response from the island’s original republicans (ie Ulster’s Presbyterians), it may be the least it can do to at least picque their interest.