For a POD, let's stipulate a stronger Reformation, and a feckless, unfocused Counter-Reformation.
Following its depopulation in the Thirty Years' War, Upper Swabia is resettled by various uprooted Protestants, including Huguenots, Waldenses, and Swiss mercenaries. The same happens in Vorarlberg and Lindau. Austria attempts to reassert control, but is repelled with French assistance. In 1803, the Act of Mediation incorporates Upper Swabia, Vorarlberg, and Lindau as Swiss cantons.
Meanwhile, Calvinism has taken hold in the Aosta Valley and the mountainous northern parts of Piedmont and Lombardy. Turin and Milan remain Catholic cities, so the Piedmontese and Lombard Protestants seek security under the Helvetic aegis. During the Napoleonic period, these regions are incorporated into the Helvetic Republic, and are finally admitted as cantons following the Conference of Vienna, joining the Confederation at the same time as Geneva, Neuchatel, Valais, and Liechtenstein.
As a result of these changes, Switzerland winds up with a much larger Italian population, and becomes a popular target for Italian revanchist sentiment. Italy makes various unsuccessful attempts to occupy the Italian-speaking cantons, the most famous of these projects being the interwar Regency of Locarno, led by Gabriele D'Annunzio.
The imminent threat of Italian invasion leads the Swiss government to tread very carefully during the run-up to the Second World War. They grant extensive privileges to Mussolini, allow Swiss fascist organizations to operate without hindrance, and actively abet Axis war operations. This proves crucial during the invasion of France, when German troops are permitted to cross through Swiss territory and skirt French defenses. The Allies blame Switzerland for the fall of France, believing that the Germans could never have successfully invaded without Swiss acquiescence. This opinion is especially strong among the French.
The Allied powers retaliate against Switzerland with strategic bombing. During the spring of 1940, Berne and Basel are largely destroyed. In the aftermath of the bombings, pro-Axis sentiment grows, and the National Front enjoys renewed popularity. The fascist army officer Arthur Fonjallaz seizes power in Lugano, declaring himself "Governor of Italian Cisalpina".
After Hitler's conquests in Poland and France, Mussolini is desperate for a triumph of his own, and diverts some of his forces from Italian-occupied France to enter southern Switzerland in support of Fonjallaz's coup. Hitler is furious, and responds by diverting troops from the zone nord to "protect" the German-speaking cantons. These are organized into Reichsgaue Welschland, Alpenland, and Oberrhein. Hitler's Swiss henchmen include Franz Burri, the gauleiter of Alpenland, and the American-born Ernst Leonhardt, who becomes Goebbels' man in Zurich. Leonhardt is instrumental in the 1942 remake of Wilhelm Tell, in which the Swiss hero does battle with Jewish burghers.
Switzerland becomes a hotbed of resistance activity, culminating in the assassination of Ernst Kaltenbrunner during a visit to Lucerne. The Italian zone is in even worse shape, due to the heavy-handed and immensely unpopular administration of Arthur Fonjallaz. In 1943 he is replaced by Ettore Bastico, formerly commander of Italy's troops in Libya.
After the Kingdom of Italy leaves the Axis, Germany occupies the entire Swiss territory, though the Italian-speaking south is officially a part of the Italian Social Republic. It is the scene of intense partisan activity and bloody repression by the likes of Pietro Koch, who is captured and killed by Swiss partisans in St Moritz in January 1945. Mussolini meets a similar fate in April when he attempts to flee north through the pass at Montespluga. Captured alive by Swiss partisans, he is lashed to a fir tree and pelted with snowballs, then left to freeze to death overnight. Grisly photographs of the "Schweizer Baumschmuck" harden Hitler's resolve not to be captured alive.
By the end of 1945, most of the Italian-speaking cantons have been liberated by the American Fifth Army, which enters Lugano on April 29. But the German and French cantons remain in Nazi hands until the very end of the war. A few pockets of resistance are not mopped up until June, owing to poor communication in the mountains.
The Allied leaders agree that a strong, unified Switzerland will be a stabilizing influence in Europe, a means of blunting both Italian and German nationalism. They propose to extend Switzerland's southern border to the Po River, and southeast to the Adige. As a demographic counterbalance, its northern border is to be extended to include South Baden, Swabia, and Alsace, so as to encompass the entire Alemannic-speaking region. A series of plebiscites are held in these regions. With the exception of Alsace, the Alemannic corridor votes to join the reconstituted Helvetic Confederation; in the south the vote is split, with Turin voting narrowly to join Switzerland and Milan voting narrowly to remain in Italy. This process of enlargement is acrimonious and protracted. The last of the new cantons, Turin, is not formally admitted until 1959.
After its post-war enlargement, Switzerland covers an area of approximately 90,000 square kilometers, more than double the size of the Old Swiss Confederacy. By the year 2000, its population has reached sixteen million, with German-speakers accounting for 50%, Italian-speakers 40%, and French-speakers 10%.