LAUSANNE, Switzerland—On a recent morning, Andrea Caruso set up a white gazebo in a square in the middle of this picturesque Swiss city and draped it with a flag from Sardinia, the Italian island, superimposed on the white-on-red Swiss cross.

He then spent about five hours answering questions from a small crowd of curious onlookers about one of the most quixotic secessionist campaigns in recent memory: a plan to persuade the Swiss to annex Sardinia and make it the Alpine country’s 27th canton.

“Sardinia is not Italian,” said Mr. Caruso, who handed out pins and stickers to promote his cause. “In Sardinia, people want to be Swiss.”

Welcome to “Canton Marittimo,” or “Canton of the Sea,” a bid by Mr. Caruso, a 51-year-old dentist from Sardinia, and his comrade Enrico Napoleone, a car dealer there, to liberate Sardinia from Italy and tether it to Switzerland.

Their proposition: Mountainous Switzerland would finally gain access to the sea. In exchange, Sardinia would receive a slice of Swiss cash to realize its full potential as a glitzy Mediterranean resort.