Do you know which Orthodox Churches allow three divorces?
All of them, the legal compromise worked out eventually prohibited a fourth marriage, it never addressed the issue of divorce, you can have as many of those as you'd like (though practically limited to the number of marriages, which is actually four in rare cases, but the fourth is only allowed for a childless widower older than 30 and younger than 40).
The legal basis was the 9th Novel of Emperor Leo le sage
, which prohibited fourth marriages (said nothing of divorce), though ironically it was also the same Leo IV who entered into a fourth marriage (it's good to be king). After his third wife died leaving him no surviving male heir and convinced that one was necessary to prevent the Empire from decending into another violent struggle for the throne as it had seen in the previous century sought to gain one. Not wanting to directly confront the law written and promulgated by his own hand without good cause, he first took a Mistress, the famed Zoe Carbonopsina. When he did have a son by her (the future Emperor Constantine VII) he decided that it was worth the effort and struggle to circumvent his own law to legitimize the marriage with Zoe (in hindsight, a pretty good decision considering Emperor Constantine VII was a good Emperor one of the greatest scholars the Empire ever produced, apparently Leo had pretty good genes, considering the intellectual successes of the Macedonian dynasty which no doubt would have lasted even longer had the Empress Zoe not been forced to be so aggresive and make so many enemies in order to merely maintain her throne, but that speeks more to the damage misogyny caused the Empire than the failures of the dynasty).
The Patriarch Nicholas Mysticus agreed to baptize Constantine, but demanded the Emperor separarte from Zoe, understanding the problems this would cause for the transfer of power and the violence and bloodshed that would inevitably follow, Leo declined and was married to Zoe by a Latin priest in the city three days later. Patriarch Nicholas objected and Leo sent out an appeal to the other four Patriarchs, Rome, Alexandria, Antioch, and Jerusalem all sided with the Emperor Leo against Nicholas who had plotted against Leo in the past and Leo determined Nicholas was simply using this as an excuse to plot against him again and was forced to abdicate, Euthymius was then consecrated Patriarch of Constantinople and gave his blessing to the marriage.
Upon Leo's death his brother Alexander became Emperor Regient for Constantine, Alexander deposed Euthymius, dismissed the admiral Himerios, and imprisoned Zoe in a nunnery, then recalling Nicholas attempting to use the marriage issue to depose the young Emperor Constantine VII and secure the throne for himself. He died 13 months later, officially of 'exhaustion', but also fulfilling his brother's prophecy that he'd reign for 13 months, many historians believed he was poisoned as he was an incompetent Emperor with many enemies in the Imperial Court. He left the Patriarch Nicholas Mysticus as Regent of the Emperor over the 7 year old Emperor Constantine VII who had been co-Emperor since the age of 2. Zoe was eventually able to secure enough political support in the Imperial Court despite her imprisonment to force Nichoals to abdicate is Regency and coronate Zoe Empress of Rome and Regent to Constantine VII. The struggle between Euthymius and Nicholas caused an internal schism in the Church of Constantinople for eight years and was not ended until the Tomos of Union in 920. Three years later, union with Rome, which had been broken off in 912 by Nicholas when restored to the Patriarchate, was reestablished by Nicholas under the direction of Emperor Constantine VII and co-Emperor Romanos I (Constantine's father-in-law).
In the Council of Constantinople in 920 (the council that, along with Imperial Authority, drafted the Tomos of Union), Nicholas was forced to issue a posthumous decree that validated Leo's marriage to Zoe and the ecclesiastical law on multiple marriages was established. They were limited to three, but the exception of a Widower over 30 and under 40 was also established (Leo was 39 when he demanded a fourth marriage), which continued as Canon Law, Ecclesiastical Law, and the Civil Law of the Empire.