protected function update( $value ) {
    if ( $this->is_updated ) {
      return;
    }

    $this->is_updated = true;
    $is_placeholder   = ( $this->post_id < 0 );
    $is_delete        = ( false === $value );

    // Update the cached value.
    $this->WP_Customize_Nav_Menu_Item_Setting::value = $value;

    add_filter( 'customize_save_response', array( $this, 'amend_customize_save_response' ) );

    if ( $is_delete ) {
      // If the current setting post is a placeholder, a delete request is a no-op.
      if ( $is_placeholder ) {
        $this->update_status = 'deleted';
      } else {
        $r = wp_delete_post( $this->post_id, true );

        if ( false === $r ) {
          $this->update_error  = new WP_Error( 'delete_failure' );
          $this->update_status = 'error';
        } else {
          $this->update_status = 'deleted';
        }
        // @todo send back the IDs for all associated nav menu items deleted, so these settings (and controls) can be removed from Customizer?
      }
    } else {

      // Handle saving menu items for menus that are being newly-created.
      if ( $value['nav_menu_term_id'] < 0 ) {
        $nav_menu_setting_id = sprintf( 'nav_menu[%s]', $value['nav_menu_term_id'] );
        $nav_menu_setting    = $this->manager->get_setting( $nav_menu_setting_id );

        if ( ! $nav_menu_setting || ! ( $nav_menu_setting instanceof WP_Customize_Nav_Menu_Setting ) ) {
          $this->update_status = 'error';
          $this->update_error  = new WP_Error( 'unexpected_nav_menu_setting' );
          return;
        }

        if ( false === $nav_menu_setting->save() ) {
          $this->update_status = 'error';
          $this->update_error  = new WP_Error( 'nav_menu_setting_failure' );
          return;
        }

        if ( (int) $value['nav_menu_term_id'] !== $nav_menu_setting->previous_term_id ) {
          $this->update_status = 'error';
          $this->update_error  = new WP_Error( 'unexpected_previous_term_id' );
          return;
        }

        $value['nav_menu_term_id'] = $nav_menu_setting->term_id;
      }

      // Handle saving a nav menu item that is a child of a nav menu item being newly-created.
      if ( $value['menu_item_parent'] < 0 ) {
        $parent_nav_menu_item_setting_id = sprintf( 'nav_menu_item[%s]', $value['menu_item_parent'] );
        $parent_nav_menu_item_setting    = $this->manager->get_setting( $parent_nav_menu_item_setting_id );

        if ( ! $parent_nav_menu_item_setting || ! ( $parent_nav_menu_item_setting instanceof WP_Customize_Nav_Menu_Item_Setting ) ) {
          $this->update_status = 'error';
          $this->update_error  = new WP_Error( 'unexpected_nav_menu_item_setting' );
          return;
        }

        if ( false === $parent_nav_menu_item_setting->save() ) {
          $this->update_status = 'error';
          $this->update_error  = new WP_Error( 'nav_menu_item_setting_failure' );
          return;
        }

        if ( (int) $value['menu_item_parent'] !== $parent_nav_menu_item_setting->previous_post_id ) {
          $this->update_status = 'error';
          $this->update_error  = new WP_Error( 'unexpected_previous_post_id' );
          return;
        }

        $value['menu_item_parent'] = $parent_nav_menu_item_setting->post_id;
      }

      // Insert or update menu.
      $menu_item_data = array(
        'menu-item-object-id'   => $value['object_id'],
        'menu-item-object'      => $value['object'],
        'menu-item-parent-id'   => $value['menu_item_parent'],
        'menu-item-position'    => $value['position'],
        'menu-item-type'        => $value['type'],
        'menu-item-title'       => $value['title'],
        'menu-item-url'         => $value['url'],
        'menu-item-description' => $value['description'],
        'menu-item-attr-title'  => $value['attr_title'],
        'menu-item-target'      => $value['target'],
        'menu-item-classes'     => $value['classes'],
        'menu-item-xfn'         => $value['xfn'],
        'menu-item-status'      => $value['status'],
      );

      $r = wp_update_nav_menu_item(
        $value['nav_menu_term_id'],
        $is_placeholder ? 0 : $this->post_id,
        wp_slash( $menu_item_data )
      );

      if ( is_wp_error( $r ) ) {
        $this->update_status = 'error';
        $this->update_error  = $r;
      } else {
        if ( $is_placeholder ) {
          $this->previous_post_id = $this->post_id;
          $this->post_id          = $r;
          $this->update_status    = 'inserted';
        } else {
          $this->update_status = 'updated';
        }
      }
    }
  }