Byzantines-First oponent?

[Ibn-Khaldun]

You might also try to go against Sicily then cross the sea and go against Egypt.

You'd gain access to quite profitable ressources in Egypt (both North and South) and you could also push north towards Rome and Milan, though taking Rome might send Crusaders trough your lands.

Well, this could be an exploit but playing as Byzantine Empire I think this is allowed. Before attacking Rome and Italy wait until the Pope have declared a Crusade against Antioch. After that you have plenty of time to take Italy and reinforce it before the Pope could call a Crusade against you. You could even sign a peace and Ally with the next Pope to prevent Crusades called upon you.