Advancing partner's bid over their preempt

Advancer’s bids: After the opponents preempt and partner bids

After partner makes a direct overcall: [2H by LHO] - 2S by partner – [Pass by RHO] - ?

Pass = 0-7 points (Use the Rule of Seven).
Single raise of partner’s suit= 8-10 support points + 3+-card support
Raise to game in partner’s suit = 11+ support points + 3+-card support
Cuebid of their suit: [2H] - 2S - [Pass] - 3H = Strong raise of partner’s suit (13+ points)
A jump in another suit: [2H] - 2S - [Pass] - 4C, 4D, 4H = Splinter (singleton + support)
New suit: [3C] - 3H - [Pass] - 3S = Forcing, good 5+-card suit.
If your right-hand opponent raises his partner’s preempt: [2H] - 2S - [3H] - ?
Double = Responsive (9-10+ points, length in unbid suits, no support for partner’s suit)

After partner makes a jump overcall in a major: [2H] - 3S - [Pass] - ?

The jump overcall shows a good hand with a long, strong suit. This jump sets trumps. You cannot introduce a new trump suit.
Raise partner's suit with a few tricks or fillers.
Cuebid the ace of a new suit if you have slam-try values.

After partner makes a takeout double: [2H] – DBL - [Pass] - ?

Make a “normal” value bid of your longest unbid suit:
   Minimum bid of your longest suit = 0-8 points
   Jump in your suit (invitational) = 8-11 points
   Cuebid their suit or jump to game in your suit or notrump = 11+ points
Jump to 3NT if you have a stopper in their suit, 11-12+ points and no major-suit length.
Don’t bid notrump with very weak hands.
If the preempt was a minor, your 4-level cuebid shows both majors: [3C] - DBL - [Pass] - 4C
If the preempt was a major, your 4-level cuebid shows both minors: [2H] - DBL - [Pass] - 4H
Consider adding the Lebensohl 2NT convention to your system to help you describe your strength.
If you’re considering passing for penalties, use the Rule of Nine:
Add: Level of their bid (2 or 3) + # of trumps you hold + # of trump honors (10 or higher).
If the total is 9 or more, you can consider passing for penalty.

After partner overcalls 3 of their suit (cuebid): [2H] - 3H - [Pass] - ?

Bid notrump if you have a stopper in their suit, even if you have another long suit.
With no stopper, bid your cheapest 3-card suit.

After partner makes a notrump overcall: [2H] - 2NT – [Pass] - ?

Play “system on” over 2NT: 3C = Stayman, 3D & 3H = Transfers, 4C = Gerber, 4NT = Quantitative.
If partner jumps to 3NT: [2H] - 3NT -- He could have a long running minor and shortness in your long suit. Pass unless you have slam-try values.

Notes:

If partner bids or doubles in balancing seat, he may be stretching a bit. It’s wise to have a little extra for your raises of suit bids and responses to takeout doubles.

When evaluating your hand, don’t count points for a queen or jack in the opponent’s suit.

If partner doubles a 4-level preempt, you should usually pass with a balanced hand. Bid at the 5-level only if you have extreme shape (very long suit) or slam-try values (a strong 14+ points).

After the opponents preempt, it’s important to get a plus score. When in doubt, settle for a reasonable contract instead of taking a risk to find a perfect one.