All of the main rental agencies will charge a fee for an additional driver, there may be small local agencies that do not, but none I have seen.
As others have hinted, you probably want to pony up for zero deductible CDW, you will have to purchase liability insurance, by law, from the company, or they include it. Your credit card car insurance coverage likely will not work, nearly all credit cards exclude Italy from coverage.
Will reiterate you learn about ZTLs and fines related to the Autostrada, both expensive surprises long after your trip. Any town of a largish size, you really do not want a car in, so planning an itinerary that is a mix of car and public transportation works the best, renting a car for short periods when needed.