The Realm of a Million Years seemed to be headed toward some such outcome; the permanent adoption of Atenism appeared to be giving the dynasty a new dynamism and provided a sort of cultural ratchet effect whereby conquests outside of Egypt proper were being drawn into an extended super-state. Sadly that TL appears to be many years comatose and presumably dead.
Oh well, perhaps it is merely going to be millions of years between posts?
Anyhow I suppose there are technical limits in any age, and that perhaps there was simply no way for an Egyptian age dynasty to conquer all of the Med Shores. To be sure all it seems to require is a seafaring technique good enough to span the Mediterranean end to end, and an Egyptian state with sufficient population to project strong enough control over closely enough spaced port bases to effectively cover the shoreline; given the lack of sophistication of native resistance on the various shores this seems doable, but one has to count the Egyptian population accurately, then deduct the large portion of them who must stay at home to sustain the core state, and estimate how much coverage of the shores the remnant available for foreign adventures could provide.
Also there is the matter of fission--the more spread out Egyptian power is, the more likely some local viceroy decides he is capable of seizing the Pharaoh role for himself and tears the empire up in civil war. Or warlords might decide to hell with orders from Egypt, identify with local powers, and form breakaway kingdoms of their own.
Communication speeds matter even if it is technically possible for Egypt to control the shorelines; the slower they are, the more tenuous the scale of trade contact, the fewer bonds there are tying local commanders to Egyptian authority.
The OP seems to be saying something else though, which is have Egypt survive as a distinct power, not a province of someone else's empire, and for that Egyptian realm, many thousands of years after OTL's Egyptian glory days, to become expansionist. Obviously the later this happens, the more the realm has to go head to head with other contenders--Persia, the disunited but aggressive Greeks, Alexander uniting them, and then of course Rome itself as well as rivals such as Pontus. The earlier we shift it the lower the general tech level is, and the more the primary problems of an ancient Egyptian dynasty intervene.
Another thing to consider is that like China, the Egyptians tended to think of their river valley not only as the natural center of the world (most people tend to think that way) but also as a land uniquely blessed; the religion implied that people who died outside the Nile Valley region would be denied eternal life only attainable in Egypt itself. Relatively few Egyptians, including perhaps especially those of the royal and noble families, would be willing to be sent out on conquest and occupation duty.
This is why RoaMY seemed so promising; the new religion seemed liable to cut through many of the OTL restraints, and allow for an expanding bureaucracy which would incorporate non-Egyptians into a universal imperial/theocratic framework. While it also seemed Atenism would promote science and technical innovation, improving the capability of the Empire to hold together over distance and time.