to get a little more content after ‘read more’ inside loop

You can get the diff between your 2 contents and then add to the first one a given number of words like this (not sure, but give it a try 😉 ) :

global $more;
$more = 0;
$content_cut = get_the_content( '' );
$more = 1;
$content_full = get_the_content();

// Get the diff
$content_diff = str_replace( $content_cut, '', $content_full );

// Get 10 first words
$some_more_content = wp_trim_words( $content_diff, 10, 'link_more_here' );

// Add it to the end of cut content
$content_cut .= $some_more_content;

echo $content_cut;

The linl_more_here parameter is optionnal and is normaly a tag with the permalink of your current post.