How to modify archive query with pre_get_posts to append CPTs?

Question

If I use pre_get_posts this way

function ef_company_query($query) {
  if ( !is_admin() && $query->is_main_query() && $query->is_post_type_archive( 'company' ) ) {
    $query->set('post_type', array( 'company', 'mission', 'values', 'staff' ) );
  }
}

add_action('pre_get_posts','ef_company_query');

it seems that wordpress won't load archive-company.php but archive.php.

How should I use pre_get_posts to append extra CPTs to an archive page?

EDIT 1

I mentioned archive-company.php because I want to load the extra CPTs at URL www.website.com/company.

EDIT 2

I'm open to any solution which pulls a specific template based on the URL www.website.com/company and allows the addition of the extra CPTs (preferably via pre_get_posts, performance wise).

EDIT 3

Trying to make things more clear here!

I want to be able to load several CPTs on the URL www.website.com/company.

1. Which template should/can I use?
2. How to append the CPTs to the main query (hopefully via pre_get_posts, performance wise)?

I'm trying to avoid the use of new WP_Query() and having multiple loops in the page.

Answer 1

You seems to assume that it would grab archive for first of multiple post types. But why? Order in this case does not indicate any kind of priority.

WP seems to consider that logical as well. If you take a look at get_archive_template() the individual template will only be considered if there is only one post type in query.

Multiple post types in query will cause archive.php to load, as you are observing.

If you want to load more specific template, you would need to override that via filters as well, for example with archive_template one (dynamic one in get_query_template()).