<div class=article>
<div class=article-header>
<div class=article-quote>
<div class=quote-body>
... a bunch more HTML ...
</div>
</div>
</div>
</div>
Just one quibble over this specific example (not the broader concept, which is sound): it probably didn’t have to be div soup to begin with. Something like this may have been more reasonable:
<article>
<header>
<blockquote>
<p class=quote-body>
... a bunch more HTML ...
</p>
</blockquote>
</header>
</article>