A filter on the_content_more_link may be appropriate for you, the filter should give you full control over the more link, so you could essentially add to it, remove it, or pre/ap-pend some extra content.
Here's an example, uncomment the appropriate line to prepend or append(ie. place extra content before or after the link).
add_filter( 'the_content_more_link', 'custom_more_link', 1000 );
function custom_more_link( $more_link ) {
$extra_more = '<br />My more link extra content';
// Uncomment line below to prepend content
//return $extra_more . $more_link;
// Uncomment line below to append content
//return $more_link . $extra_more;
}
NOTE: The extra content must be stored inside the variable returned.
Further reading/examples.
http://codex.wordpress.org/Customizing_the_Read_More
http://justintadlock.com/archives/2009/07/01/how-to-filter-a-wordpress-themes-more-link-text
Hope that helps.. :)