Error when combining with custom code to order by product attribute

I have added some custom code to my theme to order the shop products based on the menu order of a product attribute (drag & drop order using the Simple Custom Post Order plugin)

add_action( 'pre_get_posts', 'jwd_modify_product_query' );
function jwd_modify_product_query($query) {
  if ( !is_admin() && $query->is_main_query() && is_post_type_archive( 'product' ) ) {
    $query->set( 'orderby', 'pa_brand' );
  }
}

// https://wordpress.stackexchange.com/a/363654/94213
// Answer by honk31
add_filter('posts_clauses', 'jwd_orderby_tax_clauses', 10, 2 );
function jwd_orderby_tax_clauses($clauses, $wp_query) {
  global $wpdb;
  $orderby = isset($wp_query->query_vars['orderby']) ? $wp_query->query_vars['orderby'] : false;

  if ($orderby && $orderby === 'pa_brand') {
    $clauses['join'] .= <<<SQL
    LEFT OUTER JOIN {$wpdb->term_relationships} ON {$wpdb->posts}.ID={$wpdb->term_relationships}.object_id
    LEFT OUTER JOIN {$wpdb->term_taxonomy} USING (term_taxonomy_id)
    LEFT OUTER JOIN {$wpdb->terms} USING (term_id)
    SQL;
    $clauses['where'] .= " AND (taxonomy = '{$orderby}' OR taxonomy IS NULL)";
    $clauses['groupby'] = "object_id";
    $clauses['orderby'] = "{$wpdb->terms}.term_order ASC";
    $clauses['orderby'] .= ", {$wpdb->posts}.post_name ASC";
  }

  return $clauses;
}

Then I get an error WordPress database error: [Not unique table/alias: 'MYPREFIX_term_relationships']

I think the issue is that this plugin is already using the term_relationships table, so without an alias, it’s not possible to join the plugin’s code with this code.

How can I get it to work?