Creating secondary and tertiary su menus separate from main menu and dynamically

I need to create 3/4 level split menu.
The standard wordpress menus nest all the sub pages menus as a ul items within each li item.

I would like the sub menu to be a separate item in the source and site under the main menu.
it should basically read in all the sub pages as menu items.

i also want to create a tertiary menu based on the same principal.

I found this code on the forum in this post: https://www.ads-software.com/support/topic/creating-sub-page-menu?replies=5

<!-- Main Menu -->
<div id="mainmenu">
	<ul>
	<?php wp_list_pages('sort_column=menu_order&depth=1&title_li='); ?>
	</ul>
</div><!-- / Mainmenu -->

<?php
  if($post->post_parent)
  $children = wp_list_pages("title_li=&child_of=".$post->post_parent."&echo=0");
  else
  $children = wp_list_pages("title_li=&child_of=".$post->ID."&echo=0");
  if ($children) { ?>

<!-- Sub Menu -->
<div id="submenu">
  <ul>
  <?php echo $children; ?>
  </ul>
  </div> <!-- / Sub Menu -->

  <?php } ?>

But this is only for a secondary menu and I cant get it to work for a 3rd or 4th menu (it nests them again within the li’s)

Does anyone know how i can get thsi to work?