I don't know about the options specifically at Linate.
In general, when you use a search engine like Kayak or AutoEurope or Booking.com, it will return a lot of Italian-only rental companies.
These have had notoriously poor reputations over the years, like claims of being charged for damages after returning the car.
But even international rental companies like Sixt or Avis are franchised to local owners, especially on islands like Corsica and Sardinia.
So they all have generally poor reviews.
However, I tend to stick with the known brands, which generally will have offices and facilities right at the airport, whereas these local brands, you have to take a shuttle from the airport to the office about a couple of kilometers away.
I've only once been dinged with additional charged after returning a rental and that was in France with I believe Sixt. In any event, my Chase Sapphire Preferred Visa covered it, after a long process of submitting documentation.
Otherwise, my theory is that even though these are all locally-owned rental offices, at least with international companies like Sixt or Avis, you can try to go to their corporate and plead your case.
Also the other consideration is that your credit card issuers would recognize these international brands but if you put in a claim against a company like Locauto or Sicily By Car, to give a couple of examples, you might have an easier time of your claim being approved.
