I started playing CK2 again a couple of weeks ago, and boy the Byzantine Empire is annoying as fuck. I don't know if I had bad luck or something changed in the last patches, but the Byzzies are blobbing again at insane rates. In my previous two games, I lost because the Byzantine Emperor pressed a claim on my empire from an obscure member of his court of from a vassal. As the Hispania Emperor I was, theoretically able to wage war and maybe win; however, they somehow became catholic, so even if I beated their armies, the Byzzies would call to arms to five or more catholic allies, and that turned the tables quickly against me.
In my last game, they became even more aggressive, taking over Italy, almost destroying the Abbasyds and then pressing a de jure claim on the Pope and ousting him from Rome. Shit got real really quickly. So what I did is to conquer the Egypt Sultanate, and then give it to the Pope, and asking him for money. With the 600+ opinion that he had on me, this was not a problem, and repeating this several times I managed to get some 6,000 gold pesetas. Then I fabricated a claim on Rome, but ended getting a claim on the whole duchy. With this I declared to war with all my retinues + vassal armies + allies + four of the most expensive mercs.
The fighting was insane, the BE combined his whole army into a 60K+ doomstack, so I had to do the same. This battle actually slowed my laptop, and I don't know if it was a bug but it was slow enough that I had the chance to bring more mercs from Spain a couple of times and for my English allies to arrive and throw their armies into the chaos. This was the final result.
Check the number of dead nobles. I actually lost my two sons (one of them my heir with Genius trait) in the war.
As expected, they tried to retake the lost duchy some years later, but lost again and then, for teh lulz, I fabricated a claim on Constantinople and took it from them. Cue to the eternal de jure war on Constantinople every ten years. I won every time, btw.
Obviously, I took advantage of a Byzantine revolt.