Muhammad Ali, and his successors, are far more successful ITTL at playing off the various European powers against each other, and able to fully break the Egyptian state away from the Turks, take Greece as a vassal/protectorate/etc., put down the Arabs, conquer the Sudan and Ethiopia, and eventually expand across the North African and East African coasts and down the Nile into the heart of the continent.
Conquering the Sudan I can see, conquering westward into Darfur and Chad from there I can see. Conquering Ethiopia? That is not going to be easy, and even if it's accomplished, holding on to a fiercely Christian nation is going to be very difficult.
It's not impossible, but Muhammad Ali's successors will have to do a lot of things right. If the Egyptians give the Ethiopians internal autonomy, freedom to practice Orthodox Christianity, and give Ethiopian soldiers a chance to participate in future conquests, it could happen.
Conquering the Sudan I can see, conquering westward into Darfur and Chad from there I can see. Conquering Ethiopia? That is not going to be easy, and even if it's accomplished, holding on to a fiercely Christian nation is going to be very difficult.
It's not impossible, but Muhammad Ali's successors will have to do a lot of things right. If the Egyptians give the Ethiopians internal autonomy, freedom to practice Orthodox Christianity, and give Ethiopian soldiers a chance to participate in future conquests, it could happen.
They tried twice IOTL. It ended badly both times.
If they could somehow pull it off though, it'd give the Egyptians entry into East Africa, where they'd likely be able to pull the various Somali sultanates and tribes into their sphere against European incursion (and Ethiopian rebels).