I was poking around idealista and other Italian real estate websites, and perhaps it's the time of year, but it seems like there were only about one percent of rentals available for people with pets, no matter the price. Is this the case year round? (And only idealista had a filter for pets accepted)
I was looking specifically in Torino, Bologna and Pisa for 2 bedroom flats, and I literally found one available rental for €1400 or less in each city.