Can I add custom css to an mu-plugin?

You can actually put a directory for your style sheet right in the mu-plugins directory. I called mine “my-companies-assets”. The tricky part is calling your styles into your mu-plugin. In your main MU plugin file…

// Setup MY AWESOME MU plugin url
// This will help if you switch to multisite some day
if (is_multisite()) {
    define('MY_AWESOME_MU_PLUGIN_URL', network_site_url('/wp-content/mu-plugins', 'relative'));
} else {
    define('MY_AWESOME_MU_PLUGIN_URL', content_url('/mu-plugins'));
}

// Then you can just use wp-enqueue_style like normal
wp_enqueue_style( 'my-mu-styles', MY_AWESOME_MU_PLUGIN_URL.'/my-companies-assets/styles.css', array(), 1 );

/**
 * The rest of your plugin code 
 * goes here
*/