I have two universities as my affiliations (one in Florence and one in Milan), but the supervision offered by my "sponsors" (two professors) is really on an "as needed" basis. I think (hope) the committees will take the individual projects into consideration when they look at the affiliations, as a history project requiring archival research and minimal supervision is vastly different than a science project requiring the use of lab space. At least for my project, close supervision will be more of a hindrance than a help.