Katie Holmes has quite a few male admirers. A source on the set of her latest movie, the Spike Lee-produced “Mania Days,” tells us she’s been asked out seven times: “They were crew members and extras just chancing it. It really got on the nerves of director Paul Dalio. Needless to say, she said no to everyone.” While the film centers on the romance between two manic-depressives who meet in a psychiatric hospital, Holmes has been quiet on the dating front since splitting with Tom Cruise last year.