It looks like I have to add a category for full CMS’s with a sufficient layer of abstraction to build sites other than a blog, wiki, or Slashdot clone. The three that have been mentioned in comments are:
EZPublish is a PHP/MySQL CMS that looks like it does all the right things, and you can get it as an abstract framework, or preconfigured for more structured sites. However, the one (undisputed) review that I have been able to find says that EZPublish is crufty and slow.
Bricolage is aparently the open-source evolution of Salon’s CMS, using Perl and MySQL. Personally, I’m leery of Perl, which I don’t know, and PostgreSQL, which I don’t use and can’t pronounce. But it looks like a mature and exciting alternative[too-short eWeek review].
Typo3 is abstract and uses PHP and MySQL. However, I’m having a really hard time understanding it by reading the site, which is badly organized and poorly documented. The site itself says it takes weeks to learn how to use Typo3.
If you’re looking for a CMS with a greater level of abstraction, you’re going to need to spend more time on your decision. I’d probably install both Bricolage and Typo3 and get to know them both.