How to dynamically add datafields/profiles in form?
There's no way to dynamically add fields without custom code to a profile - and that code sounds onerous.  There's a better way, though: I'd recommend creating a CiviEvent and enabling "register multiple participants" from there.

You've tagged this "Wordpress", which rules out using Drupal Webform with CiviCRM integration.  That's another alternative for anyone else with a similar issue using Drupal.