To extend the OpenID Discovery API, you have the option to use WordPress’s filter API. Below is an example of how to extend the OpenID Discovery API and add a new parameter to the response of “new_value_key”.
function modify_openid_discovery_api( $return ) {
$return['new_discovery_value'] = array(
'new_value_key' => 'Some value'
);
return $return;
}
add_filter( 'wo_openid_discovery', 'modify_openid_discovery_api' );