Escapes from 1NT doubled at level 2

ais523

A player recently asked me what defences were allowed to an opponent's double of a natural 1NT opening at level 2. I checked the Blue Book, and it doesn't seem to mention this situation at all.

1NTX escapes are often very complicated, so might in a sense be considered undesirable for new player events. (As an example, "1NT, (X), 2!c = clubs or red suits" is a defence that's sometimes seen, and has a lot in common with the sort of convention that's banned as an opening bid at level 4, and is banned as an overcall of 1NT at level 2.)

Are there limitations on what sort of escapes from 1NTX are allowed at level 2? If so, what are they?

Robin_BarkerTD

This sentence

All the standard responses are permitted, but (apart from negative responses to a Strong 1C opening, or a catch-all 1NT response) artificial weak bids in response to a one-level suit opening are not.

Implicitly allows all responses to an opening 1NT, whether the next player passes, doubles or bid.