Switzerland becomes the Prussia of Italy?

I know Switzerland is divided between German, French, and Italian speaking people but could they become the nation that unifies Italy or take all of otl Italy at least north of the Papal State? The nation was heavily militarized at one point and didn’t go neutral path until major military defeats. Could they expand into Italy maybe starting with the Italian Wars? Could they become a heavily militarized republic(Prussia level) but under heavy influence by enlightenment ideas? Could they expand the canton or confederation system across Italy? Could they take French lands east of Rhône?
 
Don’t get me wrong but it looks as if it would have Austrian Problems combined with Prussian solutions: Prussian solutions being, in the analogy, a heavy militarization and enlightenment ideas shaping policy, and Austrian problems being linguistic diversity, geographical obstacles and states that were powerful contenders to do just that.
 
Don’t get me wrong but it looks as if it would have Austrian Problems combined with Prussian solutions: Prussian solutions being, in the analogy, a heavy militarization and enlightenment ideas shaping policy, and Austrian problems being linguistic diversity, geographical obstacles and states that were powerful contenders to do just that.
Wouldn’t being a republic and confederation help that especially with republics being common in Italian history?
 
I know Switzerland is divided between German, French, and Italian speaking people but could they become the nation that unifies Italy or take all of otl Italy at least north of the Papal State? The nation was heavily militarized at one point and didn’t go neutral path until major military defeats. Could they expand into Italy maybe starting with the Italian Wars? Could they become a heavily militarized republic(Prussia level) but under heavy influence by enlightenment ideas? Could they expand the canton or confederation system across Italy? Could they take French lands east of Rhône?
If they get too involved in Italy, they end up at odds with the French, Spanish, and Austrians, not to mention the Papacy and northern Italian powers (Venice, Milan, Savoy, etc.) which puts their independence itself at risk, with how volatile North Italian geopolitics were. Eventually, they'll antagonise the wrong powers too many times and Switzerland doesn't have the manpower to recover after too big a loss (Sweden would be a good parallel, I'd imagine).

Taking traditionally French lands is the easiest way to ensure a future war with the French and, considering France's vast demographic advantage over the rest of Europe, that'd be suicidal for the Swiss to attempt, even if France is at its nadir.
 
Switzerland sounds to divided internally to try to exert any kind of hegemony over Italy (or other places). The lack of a monarch would also not help in terms of diplomacy.

However, for a brief period of time (1512-1515) the Swiss took control of the Duchy of Milan (via Massimiliano Sforza). This in the context of the Italian wars would probably have been untenable in the long term even with a different outcome to the battle of Marignano, but what if instead Milan had been stronger in the century before (with Gian Galeazzo hegemony not dissolving at his death for example) and had been able to become the main employers of Swiss mercenaries like France was iotl? The idea of Lombard economic power combined with Swiss martial prowess could do much to ensure continued dominion by the Duchy of Milan over Northern Italy, keeping at bay transalpine powers.

As an aside, Italy's Prussia was commonly understood to be the Duchy of Savoy/Kingdom of Sardinia, although of course it's a very minor Prussia.
 
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