I spent 2 weeks all over Italy about 4 years ago. It was May, so I'm not sure how the weather differs from September, but here goes.
I had one carry-on, my purse, and my camera bag (not sure how many/what is allowed these days). This was all pre-YLF for me, so it was terribly un-stylish, but I think it can be done given the things I/we learn here. My main reason for only doing carry-on was that I didn't want to risk it being lost in transit, but it's so nice to only keep tabs on one bag while you're going from point A to point B.
For the plane ride I wore my white jeans, sneakers, a tee, and cropped denim jacket. These were my heaviest/bulkiest clothing items, so easier to carry them on my body than in my luggage.
If I were to do it all over again I would bring this:
beige bra, black bra, 5 pair undies (wash and hang dry every night in hotel for reuse).
3 pair socks to wear with fashion sneakers (also wash, hang, reuse).
1 long-sleeve top that can be worn on it's own or layered (personal pref for color/style).
3 short-sleeve tops to layer or wear alone.
2-3 sleeveless tops to layer or wear alone (cover shoulders for churches).
2 cardigans that will go with most/all of your tops.
2 pairs long pants (I would do 1 white jean, 1 dark jean).
2 pair walking shorts
1 casual skirt
1 dressier skirt OR dress for going to nicer restaurants.
1 trench coat (hopefully weatherproof but nice-looking and lighter weight)
1 shrunken jacket/blazer, something cute to wear when it's chillier during evening stroll.
1 pr ballet flats
1 pair of comfiest sandals you can find that match most of your bottoms
1 pair fashion sneakers
I kept all of my colors so they would coordinate. My goal was to take just enough clothes to get me through 1 week with intent of washing mid-trip for reuse later on. you can pair everything differently the second time.
wear the sneakers, jacket, jeans, and bulkiest top onto the plane.
it sounds like a lot, but it can be done. try to get things that won't wrinkle, but chances are you can find an iron or a laundromat for pressing. I rolled all of my clothes into neat little sausages (like when I'm backpacking for a week). this leaves fewer corners unused. put socks inside shoes while in your bag to save space and keep their shape. once you're in a hotel room you can spread out as you wish.
i bought some clothes and trinkets while I was there. I bought a duffel bag and moved all of my dirty clothes into it. i checked the dirty clothes for the trip back, keeping my purchases close to me in my carry-on to avoid loss.
you can even ship things home from most shops while in Italy. This is handy if you're after the specialty tiles/serving dishes, Carnival masks, or Murano glass.
if you're travelling in a group you can share luggage space for things everyone might use like a small travel iron, hair dryer, toiletries, etc.