What you would need is for expansion/power projection in the Med and Levant to be unviable, while also negating any threats possibly coming from there. A Roman-style Mediterranean hegemon seems to me the most likely way to get this, although you would need to figure why they would allow for an independent Egypt. Maybe keep them contained in the Northern Mediterranean coast? Add a weak buffer state in the Levant (think late Seleucid kingdom) and you might have the right conditions.
A very interesting scenario all-around. I hope we can keep the discusion going![]()
I think the best proposition would be a Philip of Macedon lives timeline, where instead of conquering all of Persia, he shatters Persian power, taking Anatolia, and perhaps making a play for Mesopotamia, choosing to ally with an ambitious Egyptian ruler who takes the Levant and Egypt. This alliance both makes Egypt and the Hellenic Empire secure, whilst limiting the realistic Mediterranean expansion of the Egyptians. Going west to North Africa exposes Egypt to Carthage and Rome, who don't really have an interest to go East (until that end of the Med is conquered), at which point Macedonia is a closer target for Rome, and Carthage wouldn't be inclined to expand that way (without a personality change).
Which leaves the Red Sea and Arabia as the best routes for Egyptian energies.
Im afraid you are off by 150 years or so. By the time of Philip of Macedon, Rome was no where near the Mediterranian hyperpower they would become by the time of the Ptolemies, who were practically their loose vassals. At this point the romans don't even control the whole of Italy, and, most importantly, havent even got anything resembling a war navy; and they wont get one until the First Punic war. Carthage also has a very loose hold of Southern Hispania, and I have no doubts at all that an Egypt that holds the entirity of the Phoenician homelands (including an un-sacked Tyre) and the Levant can most definately take Carthage head-on in a dispute for maritime supremacy in the West Mediterranean, and win without too much effort.
Also, getting off topic, but truly conquering Mesopotamia and keeping it under Greek control while the Persian empire still exists is borderline imposible: even if weakened, it still controls the population center of the Indus valley and the Persian core. The reason for this is that Mesopotamia was conformed of many, many very independent-minded city states that had been aforded a special treatment by the emperor in order to remain loyal. Where I'm going with this is that conquering Mesopotamia while there is still a viable alternative to your rule is as much a political task as it is a military one (here is where Trajan would fail centuries later), which means that Phillip would have to either:
a) Move his capital to the east, with the understanding thet there would be continuous rebellions and uprisings, as well as a population and political climate that is receptive to Achaemenid invasion/reconquest. This would mean that practically all of this "hellenic empire"'s energies would be focused on defending their eastern border, which also means a decrease in the prosperity of the region, as the Zagros border is quite a porous one and the cities and countryside can expect to be pillaged evrytime there is a war or just for raiding's sake. The conflicts would eventually result in the greeks losing control of mesopotamia or finally deciding to end the Persians for good.
b) Give the region even more liberties than the Persians did, effectively reducing its tax income. This would however, allow the empire to focus on other places, like placing the entirety of Anatolia and Greece under their control and maybe even starting their own bid for domination of the colonies in the Northern coast of the mediterranian (which might eventually even put them at odds with Egypt). But at this point the Med region isn't reall that rich, so if they want to avoid conflict that might not really be woth it or destroying their alliance with Egypt, then the only other place to expand to is... to the east.
So as you can see, both roads wield you a high probability of conflict with the remnants of the Achaemenids. Were a conquest of Persia to happen, then the empire would become more and more streched, and who knows whether Greece would really stay loyal to and united under the Macedonians without the charisma of Alexander a true Son of all the Hellenes.