The time limit could be an issue. Not regulatory, but technical. My Italian coworkers confirm that the regulator never mentions time limit on paid parking, as soon as you pay for it (their words). The problem really lies in getting a ticket that is valid for the whole week.
I don't have reliable information for Milan, but there are possibly different ways. One is inapplicable. Two of them require being at the ticketing machine, physically.
- One was to buy "scratchy" parking tickets. These are being decommissioned in the entire country, and have been already decommissioned in Milan. You could basically buy more tickets and scratch them in consecutive date/time boxes to stack them up
- Two is to check how expensive you can buy a single ticket, by compulsively press the "+" button on the ticketing machine until you reach your desired duration or the machine's limit. Don't be surprised if the machine doesn't allow you to buy more than few hours, because average customers stay short time
- Third is to try to see if the machine allows you to buy a future ticket, so that you can use its menu to select a different start time for your parking. This way you can buy and display a stack of 5 daily tickets
- Fourth is to use a parking app, but registration could be cumbersome and might (no reliable info right now) require you to own the car, i.e. you can't buy tickets for a rental car or such as you must prove you own that license number
For the city of Milan, considered that you spoke about long-term parking, it could be worth examining a different approach. There are a few hub parkings at largest underground stations, mostly near highways. They offer daily fares and you can pay when you retrieve your car.