Create multiple menus for each parent page and use an if condition to test which is the parent page and output that particular menu.
You could keep the menu names the same as the parent page names so that any future pages created with new menus will still work.
empty( $post->post_parent ) ? $post_parent_name = get_the_title( $post->ID ) : get_the_title( $post->post_parent );
wp_nav_menu( array(
'menu' => $post_parent_name
));
not tested but something along those lines should work.
Hope this helps