I'd say it's theoretically plausible. Swiss forces were used throughout Northern Italy as mercenaries during the Early Modern era. Their last significant expansion was when they grabbed the Italian-speaking canton of Ticino from Milan. They actually managed to conquer a good deal more of Milan up until losing the Battle of Marignano to the French in 1515. Lombardy today has 9.7 million to Switzerland's 7.7, so grabbing a significant chunk of it would probably result in majority Italian and French-speaking Switzerland.