How can I change the HTML of the_content?

I know the basics of how to add a filter to modify the_content, but I want to modify the HTML in detail. Specifically, I want to find any blockquote elements and add some HTML within them. This is what I have so far;

function modify_content($content) {
  if( is_singular() && is_main_query() ) {
      //Wrap the content in a div
      $content = "<div id='wrapper'>" . $content . "</div>";
    return $content;
}

add_filter( 'the_content', 'modify_content' );

What’s the best way to go about modifying the HTML? Someone mentioned this; https://www.php.net/manual/en/book.dom.php

Is there a better way?