Upvote:3
There is no such thing as pre-defined visa types or categories limited to certain purposes in the Schengen regulations. Furthermore, many things in the regulations and other associated documents clearly show that multiple-entry visas in particular are intended to cover completely different trips.
So I am not sure exactly what the Italian authorities are thinking when they add non-standard annotations like βturismoβ but I see no legal basis for any restriction of your visa to certain purposes.