House Medici was expelled from power and exiled from Florence in 1493; they would return to power under Cosimo Medici in 1512. Your challenge here is, how can the latter be prevented with a PoD after the former? (Can it be after the death of Savonarola?) How long can the "people's republic" of Florence last, and can it prosper?
And given the answers here, what are the effects? On Italian geopolitics, European history, art history, etc?
Small nitpicks.
House
of Medici, or House of
de Medici - though with all the GOT stuff, it's easy to forget.
Cosimo wasn't born until 1519, so I'm not sure who you're referring to. His father - the mercenary, Giovanni 'delle Bande Nere' (of the Black Bands) de Medici was all of fourteen years old - and from a junior line.
In 1512, there
was no claimant to any title, Lorenzo il Magnifico had been elected as First Signore of Florence, but he'd died on 8 April 1492. Piero 'il Fatuo' succeeded him to that title, but was chased out by that pulpit-bashing Dominican in 1494. Piero, married to Alfonsina Orsini, died in 1503, fleeing from battle (IIRC), leaving two children - Clarissa (who married a Salviati, and became Cosimo I's maternal grandmother) and Lorenzo II, the duke of Urbino. Lorenzo married Madeleine de la Tour d'Auvergne and was the father of Catherine de Medici. In 1512, Lorenzo was twenty, and his uncle (Giovanni de Medici) was the pope, Leo X. However, when the pope later appointed Medici to the rulers of Florence (only in 1531), he chose Alessandro (who, according to some sources was the son of Lorenzo II's cousin, Pope Clement VII, and according to others Lorenzo's bastard by the same woman). Then there was Ippolito de Medici, who was dressed in cardinal's skirts (the bastard son of Giuliano de Medici, duc de Nemours, marquis de Soragne, a brother of Piero and Leo X). It was only after all of them died that Cosimo was chosen to be duke in 1540, only becoming grand duke in 1569.