Extra text… after read more tag

The more-Tag have a filter, you can enhance this with a small plugin like the follow example.

<?php
/**
 * Plugin Name: br after more-Tag
 * Description: Add content of var $extra_more after more-Tag
 * Version:     0.0.1
 */

! defined( 'ABSPATH' ) and exit;

add_filter( 'the_content_more_link', 'custom_more_link', 9999 );
function custom_more_link( $more_link ) {

    $extra_more="<br>"; // here add your break

    return $more_link . $extra_more;
}

If you will replace the more tag with your markup, then use a small plugin and preg_replace.

add_filter( 'the_content', 'fb_more_link' );
function fb_more_link( $content ) {

    // only on single posts
    if ( ! is_single() )
        return $content;

    // adsense code
    $my_content="<br>";

    // replace more tag
    $content = preg_replace('/<span id\=\"(more\-\d+)"><\/span>/', $my_content, $content);
    return $content;
}