Support submit handlers on the parent form?

I'd like to put a submit handler on the multiform buttons, so I can react after the whole form has been submitted. Something like this:

function mymodule_multiform() {
  $form = multiform_get_form(array('multiform_test1'), array('multiform_test2'));
  $form['buttons']['save']['#submit'][] = 'mymodule_multiform_submit';
}

function mymodule_multiform_submit($form, &$form_state) {
  drupal_set_message(t('Thanks for submitting two forms at once!'));
}