In the DSIP rule summary, I state that doubles after a two-suited bid (by either side) are for penalties. The one noted exception is that when partner makes a two-suited bid and one of the suits is unknown, an immediate double asks partner to bid the unknown suit.
When they make a two-suited bid, the situation is slightly different. Whether we know both suits or not, we don't know which suit they are going to settle in. I propose that a delayed double after they make a two-suited bid is for takeout of the suit they have now bid. This should not be confused with a delayed double of a (known) suit, which is always for penalty.
Here's an example of a hand where a delayed double would have worked better. Partner opened 1NT (12-14) and RHO bid 2NT for the minors. None were vulnerable and I held the following hand: ♠xxxx ♥Kxxx ♦x ♣KQxx.. I wanted to compete and/or to suggest a possible penalty so I doubled. Partner doubled the takeout to 3♦ and they made 5 (most probably I could have saved a trick but I thought I was squeezed). We lost 11 imps on the board. Obviously, I didn't have enough hcp to suggest a penalty double.
What I perhaps needed to do was to pass over 2NT and then double when 3♦ came around to me. Even then it's a questionable action because my club holding won't be very useful. But I think we'd have done better than -670, assuming partner takes it out to his four-card major.
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