Much inspiration comes from Zelandakh's transfer structure over 2C, but I've made some changes. The most major one being that responder is able to relay opener's shape (though there is some trouble with single-suiters). Feel free to suggest changes
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2C---
2D = "Hearts or relay". a) 4--5 hearts, INV+ (not both majors). b) Weak with 6+H. c) GF relay.
2H = "Transfer to spades". a) 4--5 spades, INV+ (could be 4-4 majors). b) Weak with 6+S.
2S = Range ask. INV hand, balanced / clubs / single-suited.
2NT = Puppet to 3C. To play 3m, or SI in a minor.
3C = INV with 5H and 4S. NF.
3D = GF with 6+H.
3H = GF with 6+S.
3S = ?
3NT = To play.
Let's start with the 2D "hearts or relay" response.
2C--2D;
2H = 0--3H. If having 3H, then minimum.
...2S = Relay. => 2NT single-suited (3C asks shortness), 3C+ 5+C and 4S.
...2NT = INV with 5H.
...3C = INV with 4H.
...3D = 5+D GF (could be canapé).
...3H = COG with 5H.
2S = 4H, but not 4-4-0-5. => 2NT relays, 3C invite, 3H sign-off.
2NT = a) Max with 3H. b) 4-4-0-5.
...3C = Relay. => 3D 6+C and shortness, 3H 4-3-5-1, 3S 4-4-5-0, 3NT 2-3-2-6.
...3D = Not sure of game if opener has 4-4-0-5.
...3H = To play.
3C = 6+C and 4D, short hearts. (we can't invite over this). => 3D NF, 3H to play, 3S relay, 4m optional RKC.
3D = 0-3-4-6. (we can't invite)
3H = 1-2-4-6 or 0-2-4-7. (we can't invite)
So there is some problems when opener have 6C and 4C, since we're pretty high. The range for our 2C opening is about 12--15, but with 6-4 shape I guess it could be lower too. Also the single-suited hands with clubs relays pretty high. I think its okay if opener has 6C, but with 7+C it is awkward.
2C--2H ("transfer to spades");
2S = 0--2S.
...2NT = a) INV with both majors (5S-4H, 4-4, 5-5). b) SI with 5S.
......3C = Min with 6+C. => 3H 5-5 majors INV.
......3D = Max with 6+C. => 3H 5-5 majors INV.
......3H = Min with 4H.
......3S = Max with 4H.
...3C = INV.
...3D = 5+D GF (could be canapé).
...3H = 5-5, GF.
...3S = COG with 5S.
2NT = a) Max with 3S. b) 4H and 3S.
...3C = INV with 4S, not 4H.
...3D = 5S, INV or SI. => 3S minimum, others NAT max.
...3H = 4-4 majors INV.
...3S = To play.
3C = Min with 6+C and 3S.
3D = Max with 4S.
3S = Min with 4S.
2C--2S (range ask);
2NT = Min.
...Pass = Bal INV.
...3C = To play.
...3new = INV single-suited.
...3NT = To play.
3C = Max (as above).
2C--2NT (puppet to 3C); 3C---
Pass = Weak raise.
3D = To play.
3H = SI with 6+D.
...3S = Fit, but no accept.
...3NT = No fit.
...4C = No fit, but very good clubs.
...4D = Fit and accept.
...4HS = Shortness and fit.
...4NT = RKC for diamonds.
3S = SI with 3+C. => 3NT NF, 4C accept, 4new shortness, 4NT RKC.
3NT = Mild SI with 3C. NF.
2C--3red (GF transfer with 6+ major);
3M = Singelton or void major.
3NT = Non-serious, 2+ support.
4C = Very good club suit.
4M = 2 card support, minimum.
Others = Cue, serious (3S over a transfer to 3H could be non-serious).