A lot depends of the meaning of the 2 opening : is it strong ? is it weak ? Is it a multi ?
When the opening is strong and you also hold a strong hand it is best to pass and see how the auction evolves.
When the opening is a multi (with weak and strong variants) and you hold a strong hand, the chances are high that the opening is weak. When there are good indications that the opening is weak, start your defence.
In general, our approach is natural : an suit overcall is a 5 card, a double promises at least a 3 card in the other suits. Yet, we put in place a special defence against 2♦ multi and we elaborate a bit on the defence against a weak 2M opening. There is also room for the "world convention".
Against 2♦ multi : Polish approach
Partly natural : an overcall is a 5 card, constructive, 2NT promises 15-18hp with stops in both majors
Partly conventional : double (by first defender) is a take-out double with respect to a weak 2♠ hand, meaning short in spades and at least a 3 card in hearts. WIth less than 3 card hearts and less than 15hp you pass for one round. If the opener holds hearts he will pass upon his partners 2♥ (P/C) . Now you can double to show your spades.
Against 2 ♥/ ♠ weak
Natural : an overcall is a 5 card, constructive, 2NT promises 15-18hp with stop in the opened major.
Double is a take-out on which his partner will apply 'Lebensohl' in order to differentiate between a constructive hand and a weak hand :
Eg. (2♠ ) X - (pass) - ?
3x = longest suit 8-11hp
3♠ = asking for a stop in ♠
2NT = weak or strong MF. The doubler must react with 3♣ (P/C).
The 2nd defender, when weak will pass or correct to 3x in his suit.
When strong : 3♠ = GF, 4c♥ , no stop in ♠.
3NT = GF, 4c♥, stop in ♠.
Against natural preemptive openings on 2 or 3 level :
Defending with 4minor :
if cuebid in a minor : 2x5c M
if 4 am : 5c am + 5c ♥ /♠
if 4 m : 5c m and 5c AM
if ZT : 2x5c m
After 2/3♣ :
4♣ =>5+♥ and 5+♠ : a cuebid on level 4 promises both majors
4♦ =>5+♦ and 5+♥ /♠ : the other minor on level 4 promises a 5+c in that minor and a 5c M
After 2/3♦ : (not multi !)
4♣ =>5+♣ and 5+♥ /♠ : the other minor on level 4 promises a 5+c in that minor and a 5c M
4♦ =>5+♥ and 5+♠ : a cuebid on level 4 promises both majors
After 2/3♥ : (weak 2, Muiderberg, ...)
4♣ =>5+♣ and 5+♠ : no minor cuebid, so natural
4♦ =>5+♦ and 5+♠
4NT => 5+♣ and 5+♦
After 2/3♠ : (weak 2, Muiderberg, ...)
4♣ =>5+♣ and 5+♥ : no minor cuebid, so natural
4♦ =>5+♦ and 5+♥
4NT => 5+♣ and 5+♦
After 3 /3NT (Gambling)
4♣ =>5+♥ and 5+♠
dub => 2x4c M