[development] postprocess theme in Drupal 6?

I'd like to override theme_page() with the following logic: first use the page.tpl.php template, as the theme normally would; then, do some special processing to the output of the template. In drupal 5 this was easy enough, in drupal 6 I can't figure out how. If you can help, please respond to http://drupal.org/node/262085. (Sorry to bother the devel list with what might be considered a support question, but I'm stumped.)