Can I prevent the user from adding more than two levels deep of terms inside of a taxonomy metabox?

Unfortunately, this is not possible, at least not safe.

The function wp_insert_term( $term, $taxonomy, $args = array() ) that handles the creation of taxonomies provides a few filters and hooks, but the only one before the creation of the term in the database is

$term = apply_filters( 'pre_insert_term', $term, $taxonomy );

As you can see, the $args provided in the creation of the term are not passed to the filter – so you have no way of checking how many levels of the taxonomy exists by looking up $args['parent'].

An ugly way of doing it would be after the term is created, hooking into the action created_term or create_term, and checking it there. I have never done this myself, and you may open up a big can of worms deleting the term after creation with no possibility of returning an error afterwards.

If the filter pre_insert_term would accept the $args as an argument, it would me no problem.

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