Starting in 4.7 using REST API – This is JumpStart specific.
On “host” site:

function get_menu()
{
    # Change 'menu' to your own navigation slug.
    return wp_nav_menu(themeblvd_get_wp_nav_menu_args('primary'));
}
//https://hosturl.com/wp-json/myroutes/menu
add_action('rest_api_init', function () {
    register_rest_route('myroutes', '/menu', array(
        'methods' => 'GET',
        'callback' => 'get_menu',
    ));
});

On “receiving” site:

function jma_child_header_menu_addon()
{
    $response = wp_remote_get('https://hosturl.com/wp-json/myroutes/menu');
    /*echo '<pre>';
    print_r($response);
    echo '</pre>';*/
    echo str_replace('null', '', $response['body']) ;
}
add_action('themeblvd_header_menu_addon', 'jma_child_header_menu_addon');

JQuery to add current classes (coming soon):