WordPress tracks which object types taxonomy applies to. This can be established on taxonomy registration or at some point after, so you shouldn’t be trying to do this too early.
The approach would be to retrieve the list of taxonomies for the native post type and use it with lower level function, which supports multiple taxonomies:
$terms = wp_get_object_terms( $post_id, get_object_taxonomies('post') );
Of course if you interested in a list of specific taxonomies you can just hardcode that as input.