I would hope that a three-state solution would work, but wait for the ubiquitous “but”...
...given the religious ideology of these sects of Islam, they would still be at each other’s throats (literally), as they demand the “other sect(s)” convert or die in order to establish their version of a “true” Islamic Caliphate.
As a neophyte amateur, probably I don’t know enough and am wrong.
Nope, you have a pretty good picture of things.