Two heads.
One head (Coat of Arms of Syria).
One head--U.S. eagle.
Seems somehow relevant. Byzantine Empire =~ Roman Empire.The double-headed eagle is a common symbol in heraldry and vexillology. It is most commonly associated with the Byzantine Empire, the Holy Roman Empire, the Russian Empire and their successor states.
Coat of Arms of Austria (Hapsburgs).
Now, could the USA have somehow come under the control of some extension or continuation of the Roman Empire or the Sejuk Turks or ..something?