[UdcaDenny]

In 2/1 Jacoby shows 4 card support with 15 points. As this respons is so rare there is an alternative with 3+ support and 11+ points.
After 2NT opener bids 3C with a minimumopening of max 13p. Responder can invite to game bidding 3D or sign off with 3 or 4 in the major.
With bad minimum opener signs off with 3 in the major and with a good minimum hand cuebid or show a sidesuit by agreement.
With 14+ opener bids a shortness on the 3-level, with 3NT shows shortness in C. Bids on the 4-level shows a 5 card sidesuit with two tophonours,
same as in ordinary Jacoby. If H is the agreed trump 4S shows a sidesuit in S which means you have 6 cards in H.
After 2NT 3 or 4 in the major shows 14+ without a shortness or sidesuit. You can decide if 3 in the major should be stronger than 4 to give space
for slaminvestigation. Please comment if you have some thoughts about this.

[Stephen Tu]

Regular Jacoby shouldn't require 15; 13 is enough.
If you want to include invitational raises, that's fine, but I think you want to have better structure:

- include more hands into the min 3c bid, maybe make it 11-14/15
- don't waste 1M-2nt-3c-3d sequence as "game try". 2nt was invitational, just bid 1M-2nt-3c-3M as your NF game try, keep 3D as FG inquiry relay so you have more room for your good hands
- don't jump to 4M like ever, if you do make it some really specific hand type with valuable information. Leave room for cue bidding when responder is very strong.

My structure looks like:
1M-2nt:
3c = mins, 3d queries, 3M = inv
3d = 5-5 hands with good side suit, 3H starts clarifications
3H = extras 16+ bal/semi-bal (3M by responder then = min GF hand no slam interest unless opener is even stronger than this).
3S = some void, extras, 3nt asks
3nt+ = specific singletons, extras

[nige1]

Stephen Tu, on 2020-July-23, 09:19, said:

- don't jump to 4M like ever, if you do make it some really specific hand type with valuable information. Leave room for cue bidding when responder is very strong.

Several Scottish pairs recently reached similar conclusions; but I don't like dead-keys on the piano, so define a jump to 4M as minimum in HCP, poor plain-suit controls, but a good 6-card suit.

[aawk]

Whatever system you like or want to play agree with your partner first and keep track what works before you make chances.

There are many ways to give meaning to 2nt for example playing for IMPS and 2/1 system combined with the loosing trick count (LTC) it could be like this :

1♥ - ?

1♠ = round forcing 4+ card ♠ and if 3 card ♥ possible being a invite or better
1nt = round forcing max 11 hcp if 3+ card ♥ possible with 10 LTC or worse
2♣/♦ = GF with 0-2 card ♥ or invite or better with 3 card ♥
2♥ = 3+ card fit 0-9 HCP 9 LTC
2♠ = invite 6+ card ♠
2nt = 4+ card ♥ invite with 8 LTC or better or 4+ card ♥ 16+ hcp
3♣/♦ = invite 6+ card ♣/♦
3♥ = 3+ card fit 0-9 HCP 8 LTC
3♠ = splinter 12-15 HCP
3nt = non splinter 12-15 HCP
4♣/♦ = splinter 12-15 HCP
4♥ = to play 4+ card 0-9 hcp 7 LTC or better


After 1♠ same system but 2♥ shows GF 5+ card ♥ and if 3 card ♥ possible being a invite or better.


examples :

1♠ - 2♣
2♥ - 2♠ = invite or better with 4+ card ♣ and 3 card ♠


1♠ - 3♥
?

pass = minimum rather 3♥ than 3♠
3♠ = to play 6+ card s
3nt/4♥/♠ = to play
rest = slam forcing for ♥

[akwoo]

The system I've played (and, with a little but not extensive thought, prefer):

1S-2N:

3C - any minimum (except see 4 level bids)
3D - non-minimum, no shortness
3H - non-minimum, club shortness
3S - non-minimum, diamond shortness
3N - non-minimum, heart shortness
4C/4D/4H - 5-5 with bid suit, minimum, concentration of values
4S - minimum, 6 spades, no shortness

(Note the 4 level bids all show hands that should accept invitations despite holding minimum high card values.)

After 1S-2N-3C:

3D - asks for shortness; responses are 3H/S/N as above with shortness, and 4C/D/H as 1st/2nd control bids without shortness.
3H - shows unspecified shortness, too strong for immediate splinter; 3S asks the shortness
3S - minimum (i.e. a limit raise). Partner usually passes but raises to 4S with 6 (and some shortness, since they didn't bid 4S earlier)
3N - suggestion to play
4C/D/H - 1st/2nd control bids
4S - to play

Bids after 1S-2N-3D are the same, except 3S now is very serious.

After 1H, we play 2S as the limit+ raise, and the whole structure above is down 1 step (except 3S is the control bid and 3N is to play, and references to "heart shortness" are replaced by "spade shortness").

[Zelandakh]

akwoo, on 2020-July-24, 18:04, said:

The system I've played (and, with a little but not extensive thought, prefer):

And mine:-

1♥ - 2NT
==
3♣ = min with shortage
3♦ = max with shortage
3♥ = min without shortage
3♠ = max without shortage
3NT = super-max with ♠ void
4m = super-max with void in m
--

Another sensible and easy-to-remember method that has not been mentioned is:-

1♥ - 2NT
==
3♣ = min with shortage (if 3♦, then rebid as per direct 3♥+ calls)
3♦ = any without shortage (with enough space to show both range and any side suit held)
3♥ = max with any void
3♠ = max with singleton ♠
3NT = max with singleton ♦
4m = max with singleton ♣
--

And in Germany, Stenberg is the preferred structure at a higher level.

The truth is that there are an enormous number of completely logical ways of organising the hands here. It is precisely because the J2NT response is so underloaded that incorporating limit raises into it is so appealing. Forcing an additional requirement of 15+hcp seems to me to be completely crazy. I am not the greatest fan of the raw J2NT structure but I think the OP suggestion has to be considered worse just for this.