Attach a click() event to the FaceBook 'Like' button?
Make a PHP (or whatever language you use) script to CURL the source from http://www.facebook.com/plugins/like.php?href=http%3A%2F%2Fwww.MySite.Com... blahblahblah
Put the source from facebook into your html page, you can then you can do whatever you like in JavaScript/jQuery with the code from Facebook.
Some examples for CURL within PHP - http://www.php.net/manual/en/curl.examples.php