Can local actions have multiple parents?
I believe it's always Many (Local Actions) to one (Parent Item) relationship as hook_menu documentation says


  MENU_LOCAL_ACTION: Local actions are menu items that describe actions
  on the parent item such as adding a new user or block, and are
  rendered in the action-links list in your theme.


If you want to change the parent of local action you can do it using tab_parent

  $items['node/%node/bar'] = array(
      'title' =&gt; 'Bar',
      'page callback' =&gt; 'bar',
      'access callback' =&gt; TRUE,
      'tab_parent' =&gt; 'node/%/foo',
      'type' =&gt; MENU_LOCAL_ACTION,
  );


Above displays action link in node/%/foo instead of node/% , tab_parent accepts single string argument... So we can rule out option of sending multiple parents using array.. For deeper analysis you can refer 

function menu_local_tasks() in menu.inc which is responsible for action items and local tasks rendering..

If you would like to see it in action both places you can try below..

As @awm pointed out in comment we can add it to other pages using hook_menu_local_tasks_alter, Here is how node module does to include node/add menu item as local action to admin/content using hook_menu_local_tasks_alter

/**
 * Implements hook_menu_local_tasks_alter().
 */
function node_menu_local_tasks_alter(&amp;$data, $router_item, $root_path) {
  // Add action link to 'node/add' on 'admin/content' page.
  if ($root_path == 'admin/content') {
    $item = menu_get_item('node/add');
    if ($item['access']) {
      $data['actions']['output'][] = array(
        '#theme' =&gt; 'menu_local_action',
        '#link' =&gt; $item,
      );
    }
  }
}


So you can do same for your own implementation using below code

/**
 * Implements hook_menu_local_tasks_alter().
 */
function YOURMODULENAME_menu_local_tasks_alter(&amp;$data, $router_item, $root_path) {
  // Add action link to 'node/add' on 'admin/content' page.
  if ($root_path == 'node/%/foo') {
    $nid = arg(1);
    $item = menu_get_item('node/'. $nid . '/bar');
    if ($item['access']) {
      $data['actions']['output'][] = array(
          '#theme' =&gt; 'menu_local_action',
          '#link' =&gt; $item,
      );
    }
  }
}


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