Sort Main Posts by Post with newest Microblog Update

I have a function that sorts posts by last modified date:

function custom_query_vars_filter($vars) {
  $vars[] = 'sortby';
  //$vars[] .= 'another';
  return $vars;
}
add_filter( 'query_vars', 'custom_query_vars_filter' );
function techslides_alter_query($query){
      $sortby = get_query_var( 'sortby' );
      if( $sortby=="modified" && !is_admin() && $query->is_main_query() ){
        $query->set( 'orderby', 'modified' );
      }
}
add_action('pre_get_posts','techslides_alter_query');

A ?sortbymodified gets added to the URL to return the sort order.

How can I modify the sort order of the posts to be by which post has the newest microblog post OR update?

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