<div class="divclass">
<span class="spanclass">Span Text</span>
</div>
<div class="class1 class2"></div>
Yes, you can. And it's simpler than you think.
HTML:<div class="class1 class2"></div>
Note that there is a space between the classes you want to implement.
Oh yeah, in your CSS files, if those two classes have conflicting declarations (e.g. class1 has a background colour of blue, class2 has a background colour of green), I'm pretty sure the second class would override the first one.