WooCommerce customer account multiple emails

There is nothing out of the box that will let you send an email to multiple email address for one account, but you can hook a function to wp_mail filter and check based on to address or subject line and add your cc/bbc to that filter, ex:

// Add extra contact info fields to user profile page
function extra_contact_info_wpa_134454($contactmethods) {
    $contactmethods['bcc'] = 'Email BCC'; 
    $contactmethods['cc'] = 'Email CC'; 
    return $contactmethods;
}
add_filter('user_contactmethods', 'extra_contact_info_wpa_134454');

add_filter('wp_mail','add_cc_bcc_to_mail_wpa_134454');
function add_cc_bcc_to_mail_wpa_134454($args){
    //try to get the user id by the "to mail"
    $user = get_user_by( 'email', $args['to'] );
    if ($user){
        //get ccs if exists
        if ( ($cc = get_user_meta( $user->ID, 'cc', true ) ){
            //explode by comma "," to allow multiple cc addresses
            foreach ((array)explode(",", $cc) as $email) {
                $args['headers'][] = 'Cc: '.$email;
            }
        }

        if ( ($bcc = get_user_meta( $user->ID, 'bcc', true ) ){
            //explode by comma "," to allow multiple bcc addresses
            foreach ((array)explode(",", $bcc) as $email) {
                $args['headers'][] = 'Bcc: '.$email;
            }
        }
    }
    return $args;
}

Now on every mail send it will check if the mail belongs to a user and if it does it will check if that user has entered cc or bcc email addresses in his profile which will be added to that mail.