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They used to be more inclined to go for old lands after LoR was released due to the imperial reconquest CB, but that was made "restored empire only". Though that might've just been my games.
I wish they replaced Byzantine Holy War with the Imperial Reconquest CB, but limit it somehow.
 
They're after Baku and the oil supply lines. Byzantium plays the long game :p.

They didn't want to repeat Hitler's mistake, best not to get bogged down at Stalingrad! :p
 
Maybe we could have a "Historic interests" modifier for certain titles to, for example, promote ERE expansion in the Levant or HRE expansion in Pomerania and to lower the chances of Ethiopia or Asturias being roflstomped (as those were poor places, the muslims had little interest in them).
Another feature from EUIV that'd be great in CK2. The missions in EUIV encourage certain realms to go for certain territory.
 
Region/title specific ambitions ala the "become king of X" ones might make the AI go in certain directions. Maybe thats something to go for?

My worry with both missions (as mentioned by Lackadaisical) or ambitions is the simple fact that they may be triggered without the proper context. Both devises are powerful tools but they can lead to non-plausible results just as much as it currently happens.
 
Region/title specific ambitions ala the "become king of X" ones might make the AI go in certain directions. Maybe thats something to go for?
Perhaps:

"Restore Syria: Incorporate Syria back into the Byzantine Empire."

Requirements:
-Is Byzantine Emperor
-k_anatolia is completely controlled

Objectives:
-k_syria is completely controlled

Rewards:
-gain 500 prestige
 
That sounds pretty fair and feasible, if it can be properly executed obviously.