The Visconti Victorious
Duke Gian Galeazzo Visconti, b. 1351
In August 1402 the armies of Milan stood at the gates of Florence. For the past twenty years the brilliant lord Gian Galeazzo Visconti had amassed a powerful array of territory in Northern Italy- bequeathed the city of Pavia at birth, he gained Milan by overthrowing his uncle in 1385, and quickly expanded east, conquering Verona, Vicensa, and Padua in quick succession, although the latter was lost to the Carraras in 1390. Despite his conquests the duke was first and foremost a shrewd politician and skilled administrator: in 1395 he secured from Luxemburg King of the Romans Wenceslaus formal recognition as the Duke of Milan, the first Visconti to bear that honor, for a sum of 100,000 florins. Visconti additionally amassed in Milan one of if not the first modern bureaucracies, the wealth of Europe's second largest city leveraged towards consolidating his vast domains.
With the north largely quiescent Gian Galeazzo turned his sights to the south, towards Tuscany and the Romagna. In the wake of Matilda of Tuscany's death in 1115 Tuscany had been dominated by a cluster of city states. Greatest among these was the Republic of Florence. As one of the largest and wealthiest independent cities Florence had begun to expand into Tuscany using the valiant mercenary John Hawkwood, and they naturally opposed any attempts at Italian unification as an existential threat to their republic, and the wealth of the city funded its opposition to the Visconti. Florence had some success in the first war of 1390-1392, but suffered defeat in the second war of 1397-1398. Sensing weakness, the rival cities of Pisa and Siena defected to the Visconti in 1399 while Lucca abandoned the anti-Visconti alliance, triggering a third and final war in 1400.
Joining Florence was the city of Bologna, strategically positioned in the center of the Romagna and the site of Europe's first university; although not as rich as Florence or as grand as Milan it was still a respectable city and stood directly athwart Milanese ambitions.
The Visconti domains, on the eve of the Sack of Florence
The Visconti did not lack for soldiers, nor allies of their own- the Gonzaga of Mantua, and the Malatesta of Rimini, sided with Milan. The emperor elect Rupert, bribed by the Florentines, descended from the Alps, but was halted outside Brescia and forced to withdraw as his army abandoned him during the winter due to lack of funds.
With the German intervention thwarted Gian Galeazzo marched against Florence's sole remaining ally, the city of Bologna. On June 26th 1402 the Milanese defeated the Florentine-Bolognese alliance at the Battle of Casallecio. In the wake of the battle Gian sacked Bologna, and marched on Florence. The city was besieged, and on September 3rd, disgruntled Florentine citizens opened the gates, admitting the Milanese troops. Florence had fallen, and with it fell the last independent power capable of opposing the Visconti.
OK, so this is my first timeline, and I'm not nearly as knowledgeable as I would like on the period, but I've always been fascinated with Italy, and 15th/16th century Italy in particular, and the opportunity to write a timeline where Milan successfully unites the north was something I'd been considering for a while. The PoD, in case you were wondering, is that Gian Galeazzo avoids whatever illness killed him OTL, and is able to consolidate his domains and pass them on to a son.