Start as OTL
1229-35, Aragon conquered the Baleares. In 1282, the infamous Sicilian Vespers happened: All French on the island were killed, Sicily became a part of Aragon. For this, France started in 1285 the Aragonese Crusade as revenge, with no success. 1290, Aragon and Egypt even make an alliance - the first important alliance between a Christian and a Muslim state.
Around 1323, Aragon acquired Sardinia.
Becoming a nobles' Republic
In 1335, the unpopular king Pere IV of Aragon was toppled by the nobles, who made the state a quasi nobles' Republic. The king now was just the nominal ruler.
Since 1350, the Canary islands were missionarized by Aragonese, after being (re-)discovered earlier.
1397/98, the Crown of Aragon was lucky: While Iberia was struck by Black Death, the country was spared and also became new home for many persecuted Jews. And since 1407 many Italians (especially from Pisa and Milan) left their country, came to Aragon (and other states too), spreading Italian art.
But 1414-18, for the first time for centuries, people in Western Europe were horrified again of "Asian hordes": A Seljuk-Barbary fleet crossed the Adria, landed near Taranto / Otranto, swept through Apulia. The king of Naples was horrified and asked anyone he can contact for help, without success. Being desperate, the king now made an alliance with Naples' old enemy Aragon, ceding Sicily officially, for once and ever, to them. The new alliance managed to defeat the Seljuks in the South. Especially their cannons helped them a lot to reconquer the cities. Only Taranto and Bari in Apulia were held by the Seljuks. In 1418, an armistice was made - but both sides planned to restart war, when the time would be right.
In 1426, king Ferran took Oran for Christianity. But 1453, Aragonese troops made the ill-advised landing in Calabria, won some battles in the beginning; but when the main army of the Seljuks arrived, they were beaten back to Sicily, however. In 1455, the Seljuks landed on Sicily, conquering it completely in 1456.
1444, Aragon and Venice defeated Florence, fearing its economical competition, destroyed its fleet, and 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 winners to give them Corsica instead, but they were not interested.
1534, Charles VIII was elected king Carles of Aragon. This forced Aragon to join the Great Occidental War, where the Quadruple Monarchy fought against France, Aragon, the Holy Roman Empire and the Tenochca. Aragon was on the winning side: 1547, in the Peace of Barcelona the Quadruple Monarchy had to cede Murcia to Aragon. Plus, they had to pay several tons of gold.
The end of Aragon
In the further decades, Aragon was ruled by both English and French elected kings; but 1599, the kings Henry V of England and François III agreed to solve their conflict in Aragon in a way that satisfied them both: Aragon was divided - Murcia and the lands south of the Ebro went to the Triple Monarchy of England-Castille-Portugal, the lands north of it, plus the Baleares, Navarre and Sardinia (which, though, was sold to Florence) to France. From now on, its history became French and Spanish history. At least, until the anti-French War, after which all of Aragon fell to Spain in the peace of Amsterdam.