How can a Fan page become a Fan of another Fan page on Facebook when there's no way to suggest a Fan to a Fan or for a Fan to Like another Fan?

You can use facebook as your fan page to like other pages. All you need to do is to click "Account" then choose "Use Facebook as Page" after that you can visit and like other fan page using your page. You can also interact with other people and pages with other fan pages. This is one of facebook's new features.