If you haven't chosen the final faction yet, I am inclined to say you should include the Caliphate.
A) Another Islamic faction never hurt anybody.
B) Though the Caliphate was militarily weak by this point, diplomatically it was still very important. Its role was similar to, though not as critical as, the Papacy. The dynamic between Shi'ite Egypt (under the Fatimids) and the Sunni Caliphate should be modeled.