I found that the Rochester Public Library has put online a directory of Italians living in Rochester in 1931. It is only about 120 pages with most of those being a list of people with their occupation and address. There is also some advertising at the front and back of the book.
Most of the names that in this book are the same as the general Rochester City directory but there are a few names not listed in the big Rochester directory. Check out the Rochester Italian directory and see if you any new family members.