Maybe I need more coffee (probably!) but I'm counting just 8 nights? 17th - 24th, departure on the 25th?
Yep, I'll vote with the rest for going directly to Rome, then Florence, and a final night in Milan. Personal preference, for sure, but I'm not comfortable being some distance from the airport on departure day of an international flight, thus the vote to stay in Milan. Malpensa is just short of an hour or so away from the city by express train so I wouldn't want to be further away than that.
We enjoyed our 1/2 day/1 night in Milan prior to a flight home a few years ago and didn't even make it to the Last Supper! What with a long stretch in a cramped airline coach seat ahead us, we took the opportunity in Milan for a long walkabout to the Duomo and some of the other attractions. Anyway, a suggested itinerary?
3/17 - arrival at Malpensa/train to Rome
3/18 - Rome
3/19 - Rome
3/20 - Rome
3/21 - morning train to Florence
3/22 - Florence
3/23 - Florence
3/24 - Florence/train to Milan
3/25 - fly home from Milan