Add class to top level menu item if it has multiple child levels

I have a WP nav menu, and I need to add a class to any top-level <li> if that item has more than one level of child items (meaning, its child submenu has a submenu too). Like this:

<ul>
    <li>Parent
        <ul class="sub-menu">
            <li>Sublink1</li>
            <li>Sublink2</li>
        </ul>
    </li>
    <li>Parent</li>
    <li class="ADD-CLASS-HERE">Parent <!-- add class to this item -->
        <ul class="sub-menu">
            <li>Sublink1</li>
            <li>Sublink2</li>
            <li>Sublink3
                <ul class="sub-menu">
                    <li>Sublink1</li>
                    <li>Sublink2</li>
                </ul>
            </li>
        </ul>
    </li>
    <li>Parent</li>
    <li>Parent</li>
    <li>Parent
        <ul class="sub-menu">
            <li>Sublink1</li>
            <li>Sublink2</li>
        </ul>
    </li>
</ul>

I’m assuming I need to use a Walker to achieve this. (I don’t want to manually add the class in the WP Menu settings.) I’ve tried working with some example walkers I found, but I haven’t been able to get the class added to the level 0 ancestor item. Thank you for any help!

Solutions Collecting From Web of "Add class to top level menu item if it has multiple child levels"

Not sure, but maybe something like this will work? Add to the functions.php.
See explanation here.

//This function is responsible for adding "my-parent-item" class to parent menu item's
function add_menu_parent_class( $items ) {
$parents = array();
foreach ( $items as $item ) {
    //Check if the item is a parent item
    if ( $item->menu_item_parent && $item->menu_item_parent > 0 ) {
        $parents[] = $item->menu_item_parent;
    }
}

foreach ( $items as $item ) {
    if ( in_array( $item->ID, $parents ) ) {
        //Add "menu-parent-item" class to parents
        $item->classes[] = 'my-parent-item';
    }
}

return $items;
}

//add_menu_parent_class to menu
add_filter( 'wp_nav_menu_objects', 'add_menu_parent_class' ); 

So if you can use Jquery you can do it like this:

$('ul li.menu-parent-item:has(ul ul)').addClass('your class');