Can the Bourbons unify Italy?

With a POD of the beginning of the War of Spanish Succession, how can the Bourbon Dynasty gain control of all of Italy as one united kingdom?
 
Maybe the best POD would be the Spanish Succession War not happening, and the little Bavarian Prince surviving. The Treaty of the Hague in 1698 granted the Dauphin Naples, Sicily, and the eventual inheritance of Tuscany (the Grand Duke at this time had only one son, who was unlikely to have any children), while the Austrians got the Lowlands. France also gained Lorraine, with the Duke there to be compensated with Milan. The Dauphin would no doubt pass his Italian dominions to the Duke of Anjou, which gives a stable base for the Bourbons in Italy.

The biggest problem with the scenario is that the Spanish didn't accept the so-called partition treaty. Charles II named the Joseph Ferdinand of Bavaria his heir, but as heir to the whole Spanish Inheritance... not just the pieces the Great Powers wanted him to have.
 
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