1204 (as OTL), Venice initiated the infamous Fourth Crusade. The Byzantine Empire was conquered, Constantinople plundered, in its place the Latin Empire founded, which got one quarter of the lands of the old Empire. Other parts went to Venice or Genoa or became independent.
An important divergence happened in 1277, when a treaty between the crusader Bohemond VII, titular prince of Antioch and the Doge of Venice for the transfer of glass making technology wasn't signed, so the transfer of Syrian glass workers and their trade secrets didn't happen. The OTL famous Venetian glass industry wasn't born.
1281-1300, the Teutonic Order had its headquarters in Venice.
Since 1339, Venice started expanding on the terra firma - a sign that its position as a sea power was declining. 1366, the city managed to defeat its old rival Genoa; however, in reality both powers had already somewhat suffered since the rise of the Rum-Seljuks and the fall of Constantinople. 1394, the Black Death arrived in Venice.
1407, Maffeo Servitore, a cunning Florentine diplomat, devised a plan. Florence, Savoy and Venice divided all of Northern Italy except Genoa into spheres of influences, which said three states were allowed to conquer. Otherwise, the big three were supposed to live in peace. Until the 1430s, this is what happened: The little city states (which were near collapse after the difficult 14th century) of Northern Italy were "mopped up" and annexed.
In 1430, Venice also annexed the patriarchate of Aquileia (which was part of the Holy Roman Empire). 1444, Venice defeated Florence in alliance with Aragon, fearing the former's economical competition. The victors destroyed Florence's fleet, forced it to sign an "everlasting treaty" forbidding Florence's ships to go to ANY harbor in Europe or the Mediterranean (except those on its own territory). In addition, Florence had to pay a big sum of money. Florence offered the victors to give them Corsica instead, but they were not interested.
Just a few years later, in 1448 Venice lost Dalmatia to the Rum-Seljuks, only kept Istria. Now, it was finally reduced to a purely Italian power. In 1490, Charles VI of France could force the Republic to appoint his cousin Jean "protector of the republic", essentially giving him lots of real power, promising them an "everlasting alliance" with France against the Muslims. Until the end of the republic, the French protectors wielded the real power in Venice. (This wouldn't stop the Seljuks from taking Cyprus in 1496, however.) In the Occidental-Seljuk War 1519-22, the alliance of the Quadruple Monarchy, Florence, Venice and some German princes fought the Seljuks to a stalemate along the Po river, which became the new northern border of the Seljuk empire.
1511, Venice had joined the "Alliance des Alpes / Alpenbund" with France, Bavaria and Württemberg-Carinthia, which was mainly directed against the Seljuks. This didn't stop the latter from conquering Crete in 1521, which meant the de facto end of Venice as a sea power.
1567, France, Venice and the HRE united for the first French-Seljuk War against the weakened Seljuks. In the peace of Krems (Austria) 1574, the Seljuks had to cede Dalmatia back to Venice. They also participated in the Great Seljuk War 1599-1604, gaining the Ionian islands and Crete in the peace of Naples}}. In 1631, when Florence annexed the duchy of the Marches, Venice as France's ally was allowed to annex the more valuable North: Bologna, Ferrara and Ravenna. After the Second French-Seljuk War (1635-46), they also gained the Peloponnes in the peace of Györ. And when they participated in the Luxemburgian War of Succession (1660-64), they gained southern Tyrol.
During the years 1660-67, Florence and Venice waged war against the Seljuks, despite the fact that France didn't fight with them, but they expected that the Seljuks were beaten after their latest defeat by Russia. Instead, they were defeated, losing their conquests from the peace of Györ. After the victorious Third French-Seljuk War (1668-74), Venice received the Aegean islands in the peace of Belgrad.
In the Anti-French War (1682-94), Venice had chosen the wrong side, however. 1688, the new kingdom of Florence-Sicily/Italy entered the war on the coalition's side, invaded Venice and Savoy. In the Battle of Mantua October 1688, the Armies of Savoy and Venice were defeated and driven back. The Peace of Amsterdam gave Milan and Ravenna to Italy, to drive a wedge between Savoy and Venice. The Alliance des Alpes was dissolved.
1761, the protector of Venice died. Traditionally the new one had to be appointed by the French king, which couldn't happen due to France lacking a king. Italy used the opportunity and annexed Venice, including Dalmatia, since France was distracted. The Seljuks also stroke, took the Venetian islands in the Aegean.
Part of Italy