I've worked with Bare in Italy before, AFAIK, the entity that pays you depends on your address, not the place where you perform the shop. So for example, if you have a US address, they will pay you like if you had done the shop in the US and probably report it the same way for tax purposes (US HQ will pay you). If you have an Italian address, their european branch in Belgium will pay you... As for the legality of working there, if this is an American MSC, you're performing a job for your MSC at home, you're not being employed in Europe, so you should be fine.
AQ also works there, but they take more than 3 months to pay so I don't recommend them. Ipsos also has a branch in Italy and I used to work for a Polish company named lagom, which is based in Poland... I had Italian residency at the time but they would send me sometimes to other countries (mainly switzerland) when they needed shops to be done and there was nobody to do them, I didn't have a trouble with those either... Also, they won't bother for the couple of hundreds euros you might earn at the most...
edit: most of the shops require local language skills, although not all of them.
Edited 1 time(s). Last edit at 10/30/2018 01:46AM by aldoman.