A couple of thoughts from last night.
First, Super-accepts after transfers. With a very tight range available to Opener, the most likely problem for Responder more and more seems to be the two-suiter hand. A case in point for the opponents last night was a Responder holding 5-5 reds, K10xxx in each, with xx-x outside. Opener has 5-3 and 5-5 support for the reds, with AK-A outside, so six of either makes (5-5 in hearts).
Opener did super-accept, but their call blew up the auction.
I think a reasonable structure would be:
+1 = I have a hand where a stiff would be interesting (meaning, a hole suit)
E.g., 2NT-3D-3S or 2NT-3H-3NT
If Responder hears the +1, he is forced into shortness-based slam tries below game. He bids 4C with club shortness, 4D with diamond shortness if the agreed suit is spades, 4H for diamond shortness if the agreed suit is hearts, 3NT for spade shortness, 4S for heart shortness, and re-transfers. Responder can also re-transfer and then cue above game if he wants to know the hole for control reasons.
This +1 option keeps the hole secret for as long as possible.
The other option is a fit-oriented call. Opener bids suits up the line across from which he would accept a slam move if Responder had so moved, with 3NT after heart agreement being a spade-acceptance call. This strongly implies control of all suits, but the call might mean that one suit features KQx or Qxx or something fit-dependent. If Opener bypasses a suit Responder has, Responder on shady slam interest can resign. If Opener has not yet reached a suit, Responder can introduce it, with re-transfers but not re-transferring showing the re-transfer suit. Opener also does not bid the re-transfer suit, instead bidding the agreed suit at the four-level with only slam acceptance for the agreed suit and the re-transfer suit.
I kind of think this would work better.
The other thought is a brainstorming idea of having 2NT-P-4C show 5-5 in the majors, with Opener bidding 4D if he prefers spades. If Opener bids 4D, Responder re-transfers. This might seem silly, but there is a reason. Doing it this way allows 4C to be mutli-purpose, as 4C...4S makes little sense otherwise, no matter what major Opener picks. I'm not sure what purpose this would serve, but I just thought I'd share the idea because it seems to be an interesting occurrence. With some partners, I play that a 2S response to a 1NT opening shows one or both minors, with opener bidding 2NT if he prefers diamonds, and this works wonders. This seems like a theme, where a call two below two suits asking for Opener's preference of the two suits and Opener bidding next-up to show the higher preference allows space for the "asker" to have only one of the two suits in reality. This same type of auction could happen after 2NT-P-3S.
Another example of this struicture might be a 2C overcall of a 1NT opening showing one or both majors, with Advancer bidding 2D if he prefers spades. That would allow Overcaller to know which major is best in the two-suiter scenario and to not be preempted in the one-major scenario. That might also allow for an interesting approach over a weak 1NT opening:
2C = weak with one or both majors
2D = strong with both majors
2H/2S = strong with the indicated major
2C as both majors OR one major and a minor. Advancer picks the major (2D for spades). If Overcaller had both majors, he goes to where Advancer likes. If he has a major-minor, and if Advancer prefers his major to the other major, we play in the major and the Opponents are lost. If Advancer picks the wrong major, the 2D call is low enough for Overcaller to bid the other major as Cappelletti. 2M immediately is one-suited; 2D immediately is majors, stronger.