How to add extra arguments/parameters to ajax callback function?
Drupal doesn't have a mechanism to do that, no. As mentioned in the post you linked to, there's no need to pass that data to Javascript and then back to PHP though - just keep it in the form:

function mymodule_form($form, $form_state) {
  $form['button'] = array(
    '#type' =&gt; 'button',
    '#ajax' =&gt; array(
      'callback' =&gt; 'my_callback_function',
      'wrapper' =&gt; 'my_target_area',
    ),
  );

  $form['#foo'] = array($group1, ...);

}

function my_callback_function($form, $form_state) {
  $arguments = $form['#foo'];
  return $form['my_target_area'];
}