Just a fun little idea I came up with, despite my personal dislike of the Republic of Venice.
What if, with a POD of past 1204 AD, Venice had, like Rome before it, transitioned, by itself, without (or with little) intervention from outside powers, from a republic to a monarchy? To my mind, this could be either a principality, duchy (I think the word doge has the same roots as duke) or a kingdom as granted by either the Pope or the Holy Roman Emperor, or, in the most extreme case, get a Venetian elected as Holy Roman Emperor. Or even, depending on how much Italian land they hold at the time, during the/an age of nationalism, leading to the Venetians leading a different Italian unification and declaring themselves a kingdom or empire.
Any thoughts? Which seems more likely?