Cultural effects of a 1000-years-old Macedonian Empire

Of course the easiest POD is Alexander surviving (perhaps a POD some years before also works) at least until the age of his son(s) is suitable for rule. This likely means campaigns in Arabia and probably the West as well.
Then, you have to devise policies to keep the thing together, and this means integrating Iranians and Graeco-Macedonian elites as Alexander intended and the Diadochoi largely ended up not doing (resulting in, ahem, problems). Also, fixing the poisonous court and establishing a way to maintain a stable center, both in terms of administrative efficacy and, critically, a form of legitimacy that allows peaceful, orderly successions and general acceptance of the unity of the empire. This takes time and requires capable rulers.
In due time, of course, a lasing Argead dynasty would hve tradition and inertia on its side; but at first, they (and the Successors) ruled mostly because of the military power they had, and the semi-divine aura this implied. Alexander was a conqueror. You need something more than army's loyalty to keep the whole affair going.
I was thinking about a POD like this, but "1000-year-old Macedonian Empire" that i proposed wouldn't necessarily be ruled by only one dynasty in its entire history. It only needs that the successor dynasty to be of helenic/macedonian origin (ptolomeu's descendants, for example) and to keep most of the territory
Fine, but a longer-lived Argead rule is probably needed to entrench the thing.
I actually can see a system vaguely resembling the Iranian Empires where the ruling dynasty is associated with a few higher noblility houses which could (and a times, did) stake claims to kingship themselves (notably the Mihranids in the late Sasanian period, but they are not the only case). In this case, descent from the generals and relatives of Alexander would be a prestigious title. The problem is that such a system, while it served the Iranian empires fairly well, is likely to map into instability when translated to the notoriously quarrelsome Macedonian aristocracy... but I suppose the scenario allows for periods of fragmentation and civil wars.
A surviving Macedonian Empire need a longer living Alexander and an heir born by Stateira or Parysatis not Roxane and would be really different from the Hellenistic Kingdoms of his successors because Alexander wanted build his empire on the integration between Hellenic and Persian aristocracy, culture and traditions
 
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