Render template multiple times per page?

I’m running a Timber-based theme on a multisite. I would like to extend my site search functionality to show search results from every site in the network. I have the following code in my search.php:

if ( is_multisite() && isset( $_REQUEST[ 'multisite' ] ) && $_REQUEST[ 'multisite' ] ) {
  $search_for = get_search_query();
  $sites = get_sites();
  foreach ( $sites as $site ) {
    switch_to_blog( $site->blog_id );
    $query = new \WP_Query( $search_for );
    $context['title'] = 'Search results for "' . get_search_query() . '"';
    $context['site_name']  = get_bloginfo();
    $context['posts'] = new Timber\PostQuery( $query );
    Timber::render( $layout_template, $context );
    restore_current_blog();
  }
}
else {
  $context['title'] = 'Search results for "' . get_search_query() . '"';
  $context['posts'] = new Timber\PostQuery();
  Timber::render( $layout_template, $context );
}

Note that I’m calling Timber::render() multiple times in a single page load. Stepping through in the debugger I see the loop is executing once per site. Unfortunately, the template is only rendered for the first site.

How do I render the same template multiple times for a single page request?