I appreciate the information and your enthusiasm but I don't see how all Allegretti's can be related. That's like saying all Smith's and Jone's in U.S. are related. My Uncle went to Terlizzi in the late 1970's and told us that there are Allegretti's in that town that are not related to us, at least not directly. Did you learn any family tree information or some history?
I tried to access the web site you mention but there was no response. I don't speak (or understand) Italian so if the web site is in Italian it won't be of any help to me.
My Allegretti family settled in the NY area. What part of the country are yours from?