Create a hostedon.php file to be added to your mu-plugins folder and add this:
function mynetwork_hosted_on() {
if (is_multisite() && !is_admin()) {
$current_site = get_current_site();
if (!isset($current_site->site_name)) {
$site_name = ucfirst( $current_site->domain );
} else {
$site_name = $current_site->site_name;
}
$output = "<span class=\"footer-pipe\">|</span> ";
$output .= __('Hosted on') . ' <a href="https://'. $current_site->domain. $current_site->path. '">'. $site_name. '</a> ';
echo apply_filters('mynetwork_hosted_on', $output);
}
}
add_action('wp_footer', 'mynetwork_hosted_on');
Which will basically make the .php file you just added run everytime all the time (only in the front end) execute in every theme where the wp_footer(); code is placed (pretty much every theme), which is generally way at the very bottom. .. you can adjust to put inline CSS in there instead of a class
This will also make it so you don’t have to edit all of those themes.