AFAIK the reason Kemet never had a huge empire is that their mentality was more defensive than offensive, unlike, say, the Assyrians, whose very state was founded upon the idea of Universal Empire.
The Pharaoh in the Middle-East was a hegemon figure, more like the Chinese Emperor than the King of the Universe or the Roman Emperor.
The Kemetians thought (with good reason, mind you) that they were the world's greatest civilization and the Pharaoh reigned over other monarchs. That rule of the Pharaoh was order itself and any peoples opposed to his superiority were chaos. So yeah, you need them to think like this: "Kemet is the superior civilization, and therefore it deserves to rule over all other peoples and needs to bring Order to Chaos before Chaos consumes the Gods' Order."
I think that when it comes to territories, you need at least Kush/Nubia and the Levant. I think that in order to make it strong and stable, Kemetian Syria would be perfect in order to provide a strong buffer state between Kemet and whatever power dominates Mesopotamia at the time. It does however, gets Kemet in conflict with Anatolian powers as well, such as the Hittites and the Mitani.
Another possibility: Libya. The Libyans were a headache for the Kemetians sometimes, they even invaded alongside the Sea Peoples during the Bronze Age collapse.
Cyprus is possible and would be interesting, but is the naval technology for this even there? Do they even the naval mentality? Egypt is not a good producer of woods, so they dependent on Lebanon in order to have wood for ships. Might imply that in order for Kemet to obtain naval hegemony over the Eastern Med, they need overlordship/domination of Lebanon.
Greece seems a little far-fetched. Even if the Kemetians can get forces there, are they even able to conquer the place? Especially after the Greeks invent the Hoplite system, Greek heavy infantry was the best in the world. They would be fighting a lot of bickering city-states on the end of a long supply line. Its closer than Persia was, but its still far.