Greece rather narrowly avoided becoming a republic in 1910/1911, right after the Goudi coup, ironically thanks to Venizelos himself. There was much anti-royal animus in the elites, and most especially among the junior officers (who would go on to effectively fight the Balkan Wars, WWI, Asia Minor Campaign, and provide Venizelism's military pillar) thanks to the 1897 war and the monopoly of the higher leadership by a small coterie of royalist officers. One of the first things the Military League did was to cashier the princes serving in the army. When Venizelos was called to Athens, initially as "advisor" to the Military League before becoming Prime Minister, he was considered an anti-royalist due to his clashes with Prince George in Crete. However, both due to his own tendency at the time to seek compromise, and because he knew that the monarchy was strongly backed by Britain (Greece's de facto overlord), he intervened decisively, first in preventing the 1911 Revisionary Parliament from becoming a constitutional parliament with the power to change even the fundamental articles of the Constitution, and second, once he had been named Prime Minister, by restoring the princes to the army, and by restoring Crown Prince Constantine as Inspector-General of the army (and CinC in wartime).
Irony abounds here, since without the nimbus of the Balkan War victories ostensibly "led" by Constantine, the latter would never have had the political capital to take on Venizelos... While I find it hard to believe that Venizelos would opt for a full republic with a president (given the highly factional nature of Greek politics this was a recipe for political anarchy), he certainly went the extra step (or mile) to ingratiate himself with King George when he restored the princes. If he had not done that, then the position of the throne would have been much weaker, and the National Schism would arguably have been avoided, with Greece becoming a "real" constitutional monarchy, rather than one where the king (right up to 1967) thought that he could meddle in politics.