Wrap Content After Read More Tag in Div

Is it possible to wrap the content that appears after the read more tag in a div so that it can be hidden until a jquery toggle link is clicked?

This conditional statement below works but I can’t seem to wrap any content that appears after the read more tag. I can’t for the life of me find a way to add extra markup to the read more tag. Even functions I’ve found that allow customization of the read more tag don’t seem to provide a way for me to add an opening div just after the read more tag or link.

if( strpos( $post->post_content, '<!--more-->' ) ) {

The jQuery is no problem once I have the required markup in place. Any help is greatly appreciated! Thank you