Take-Out Double over 1NT

Let's take the most frequent example we meet. Opponent opens 1NT 12-14 and partner has doubled showing middle of range or more - 13+. This 13 HCP critical value may be adjusted according to the openers strength. E.g. a 3rd/4th seat 1NT opening which is shaded to 11, double is shaded to 12! With a 14-16 opening use 15 etc.

Let's first remember what partner who doubles does NOT have
While one knows partner has 13+ HCP, one can also usually expect a somewhat flattish distributions

Responder's options following a T-O double:
Much Judgement is clearly required in this position:
The question that needs answering is this:-
Partner's double has thrown down the gauntlet and your dilemma is:
Any subsequent double by either defender following a sequence begun ...1NT-*....is a mandatory penalty double.