'#submit' attribute does not work for custom submit in hook_form_alter

I'm adding an additional button to the user_profile_form that lets them jump to different page in addition to just saving their settings (which just loads the same form with settings applied)

function mymodule_form_alter(&$form, $form_state, $form_id) {

if ($form_id == 'user_profile_form') {
$form['save_and_add_pets'] = array(
'#type' => 'submit',
'#value' => 'Save & Do Other Stuff',
'#submit' => array('my_custom_func'),
);
}
}

function my_custom_func($form, $form_state) {

user_profile_form_submit($form, $form_state);
drupal_goto('this/other/page');
}

The functon is never called. However, if I use $form['#submit'][] = 'my_custom_func'; in this mymodule_form_alter(), it works, but I have no way to differentiate which button triggered it ('Save' or my custom button).

Is it possible to use a per-submit button '#submit' handler in hook_form_alter()?
Is there any way to add a custom button/callback to a core form like this?

thanks