Nice building. Logically thinking, Turkey is a decent sized country and a growing economy. It needs to climb from it's current 19-20th top economy down to top 10 and then these expansion views would make sense. Turkey doesn't and will not have a global force of any kind, whether army, navy or air force so it doesn't make logical sense. Next to Turkey is Germany, France, on the other side KSA.....all these are bigger powers than Turkey (KSA may be at the same level but MUCH ahead money wise).
Lastly, putting all 3 military commands in one place also doesn't make sense. The Pentagon is strategic in nature, the commands are dispersed (if you must follow the US system). The US CENTCOM's HQ is on the other side of the coast in Florida many states away from the Pentagon.