Well that would require a lot of things though.
'Armenia becoming freed from Ottoman puppetry at the start.'
'Armenia not being annexed by either Georgia or Russia.'
'Greece winning the Fourth Balkan War, and for that matter the Belgrade Congress even happening, which it sometimes doesn't.'
'Greece deciding to attack the Ottomans.'
'The Ottomans being weak enough to lose, which is unlikely considering their relative strength at the start.'
All this relies on A.I decisions, as making this option only for the player seems gamey as fuck. Greece barely if ever actually does anything in KR, and a federation of that sorts seems both unrealistic, and more importantly, OP in terms of game play. I wouldn't be averse to the devs making a little event that changes the flag and name to the Byzzies though if enough people actually wanted it, but balance is key there. Your chain of events would rely on a lot of very unlikely events to occur though, unlikely even for a player of one of those nations.
1)armenia isnt required, she should just be able to join if she wants
2)i have never seen the Belgrade congress not defeating the bulgarians, but i think something should be made to make them annex bulgaria cause many times i have seen bulgaria be left with just the provice of sofia blocking the rest events of the congress
3)the ai ussualy attacks the ottomans, in the event i think there is only a 5% chance not to attack and some more chance that instead of war let the locals decide their fate, but even if u attack after the union with serbia ,another war with the ottomans will come up so u can take the whole minor asia, so the first one will only give u a foothold in ottoman teritory
as i have answered i dont think it is neither unrealistic nore unachievable for the ai
the requirments can be these
1)annex bulgaria in 4th balkan war
2)2 countries agree
-then u can attack ottomas, with romania as allie and if u are lucky enough u would do so the same time the arabians attack, capture the whole minor asia
-have some events of rebuilding the empire and move capital to constantinople, have some events for the orthodox church(like the russians)
-in ww2 u will have 2 options 1)join at the side of germany in exchange for crete(if they havent solded to u or the ottomas at the start of the game) and claim south italy
2)if the austrians join the war at the side of the germans declare war at them and get the provices of yugoslavia and give romania its west provices
-after ww2, u can have an event for attacking the arabs, so u can claim the coast of east mediterenean
i dont say this idea because(at least only because) i am greek but i think that it would be interesting to build an empire from ashes at the exact period in the exact area and many people already asked for this