The UN should arrange, as US forces leave, for an international group of peacekeepers and negotiators from the Arab countries to bring together Shiites, Sunnis and Kurds, and work out a solution for self-governance that would give all three groups a share in political power. Simultaneously, the UN should arrange for shipments of food and medicine, from the United States and other countries, as well as engineers to help rebuild the country.
But the U. S. has to be careful. If our strategy depends on Sunnis doing the fighting to clear Mosul and Ramadi - and, as near as I can tell, that is the strategy - then you have to be careful that Sunnis don't perceive the U. S. to be operating arm in arm with Iran or with Iranian-backed Shiite militias that Abadi - Prime Minister Abadi is using in Iraq, so that, in effect, we're fronting for Iran.
Sunnis consider Shias a pack of unwholesome fanatics and Shias consider Sunnis a gang of lukewarm no-goods - there's nothing like religion for spreading brotherly love!
We as outsiders can't differentiate between Sunni and Shi'ah, but leave it to them and they'll get over the difficulty by some kind of hanky panky, just as the Turks did, and for the present it's the only way of getting over it. I don't for a moment doubt that the final authority must be in the hands of the Sunnis, in spite of their numerical inferiority; otherwise you will have a mujtahid-run, theocratic state, which is the very devil.