You should use lxml. It works with multiple class values separated by spaces ('class1 class2').
Despite its name, lxml is also for parsing and scraping HTML. It's much, much faster than BeautifulSoup, and it even handles "broken" HTML better than BeautifulSoup (their claim to fame). It has a compatibility API for BeautifulSoup too if you don't want to learn the lxml API.
Ian Bicking agrees and prefers lxml over BeautifulSoup.
There's no reason to use BeautifulSoup anymore, unless you're on Google App Engine or something where anything not purely Python isn't allowed.
You can even use CSS selectors with lxml, so it's far easier to use than BeautifulSoup. Try playing around with it in an interactive Python console.