The simple solution was to NOT allow the Shia to demand an immediate handover of the government to them, but rather, to instead enforce a MacArthur Plan (as in General MacArthur dictatorship over Japan for 7 years) whereby the US maintained control over Iraq for at least a few years and...
Enforced a tripartite provisional government on Iraq with an equal say from each of the Shia, Sunni and Kurdish regions, including a Tri-Presidential office (2 of 3 votes to win on any position/ law/ etc...), an equal sharing of oil revenues between the 3 regions (Sunni are currently shut out since they have no oil), an agreement to rebuild Sunni areas as they were the areas most devastated by the US takeover (I know Sunnis/ Saddam were the cause of all angst prior to the US but gotta put them back together again, for the people, not the old political/ repressive establishment), NOT just disband the Sunni military forces (this was the cause of, first, Al-Queda in Iraq consisting of all fired Sunni officers and military personnel, and then ISIS which also was initially comprised of 95% of these fired Sunni officers and military... all done at the demands of the Shia... just... STUPID!!!) but instead start an immediate integration program to have equal representation from all 3 regions in a representative military.
I don't know if this succeeds any better, or worse, than actual history.
But I am firm in my belief that I had the correct plan, to put the country in its best possible position to succeed, rather than just giving in COMPLETELY to Shia demands... who had an OBVIOUS axe to grind with the Sunni...
Just my 2 cents.