It's quite common to play a system where opener, having four of the suit into which responder has transferred him/her, breaks the transfer in some way. Such a break is often referred to as super-accepting, and there are a variety of schemes in use:
The first question is 'Why are we doing this at all?'. Basically when we're bidding our hands, we strive to discover and announce a fit with partner. If we have support for the suit that partner opens, particularly if this is a major, we want partner to know about the fit, and how good a hand we have. And once we know that a fit exists, one important tool we have available to help us assess the combined strength of the two hands is the Losing Trick Count [LTC] - this is another topic for another day.
By super-accepting partner's transfer request, we're aiming to bring exactly the same thinking into play, and using the same tools. Once we super-accept, responder is aware of the fact that we have a fit, and can proceed in the light of that knowledge. The difference here is that opener's hand is already limited, but we still want to give responder as much useful information as possible.
Although the LTC is not a factor in opening 1NT, it comes into play as soon as opener is aware of a fit. The vast majority of 12-14 NT opening hands have either seven or eight losers, once a major-suit fit has been established. This difference of one trick is often crucial is determining whether game is on, or whether the two hands are in the slam zone. So the system described here uses two super-accepting bids, 2NT to show a 7-loser hand or better, and 3-transfer-major to show an 8-loser hand. With more than eight losers, opener doesn't super-accept at all.
Once opener has made a super-accepting bid, the ball thereafter is mainly in responder's court, unless he/she decides to consult opener further. Most of what follows assumes that opener has super-accepted with 2NT, which leaves more space for subsequent bidding, but responder is still in charge of proceedings if opener's rebid was 3-transfer-major.
Responder may be in one of several situations:
Armed with fairly precise knowledge of opener's hand following the super-accept, responder is now very much in the driving seat. With a poor hand, all he/she wants to do is to get out at the lowest possible level, i.e. 3-transfer-major, and the way we achieve this is via a re-transfer bid, i.e. if responder's first bid was 2♦ to ask opener to bid 2♥, he/she now bids 3♦ to insist on opener bidding 3♥, and this then ends the auction.
As far as possible game-going hands are concerned, responder should know enough to pick the contract. He/she simply uses the LTC of his/her own hand in conjunction with opener's announced LTC. Responder is also in a position to pick the most advantageous declarer, so either bids the final contract directly, or re-transfers and then bids the final contract in order to ensure that opener is declarer.
If the combined LTC puts us in slam zone, responder may simply want to establish that there aren't two quick losers [RKCB]. Or he/she may have a hand shape where cue-bidding is the better way forward. Or responder may want to consult opener further as to how well the hands are fitting.
The most straightforward way forward is where responder simply needs to ascertain that adequate key-cards are held, and uses RKCB to determine this. Transfer-bidding aside, the question of maximising the effectiveness of RKCB comes into play, but that's another topic for another day.
Where responder has an extremely unbalanced hand, say with a void somewhere, it's more likely that cue-bidding will be necessary, so it's essential that responder can initiate the bidding of first-round controls. I'm intending to use 3NT for this. We can rule out the use of 3NT as any kind of natural bid in this situation, so this is responder's means of requiring opener to cue-bid his/her lowest ace. The only other permissible bid is four of the agreed major, saying Sorry partner, no aces.
We then have the possibility that responder wants to consult opener, and the two possible routes to this are via splinters and trial bids. We need to be clear that responder shouldn't be using consultative bids unless there's something to consult about: we don't want to give information away for no reason.
Taking splinters first, and assuming hearts is the eventual trump suit, then over 2NT, 3♠, 4♣, 4♦ are all splinter bids [for spades, we want to be able to sign off in 4♥]. Any bid from opener other than 4-trump-suit is positive, implying either the ace of the splinter suit [and nothing else of note] or no honour cards in the splinter suit. It's up to opener to judge the most telling positive bid from his/her hand - could be a first-round control, could be some other good and likely-to-be-useful holding.
Trial bids are used in an analogous fashion to those used in responding to Jacoby 2NT. Responder is showing a decent holding in a minimum 4-card suit, and is asking opener to judge how well his/her hand fits with that. A doubleton is a poor fit unless it includes the ace or king. A better fit is Hxx or Hxxx, where the H is at least the queen and preferably the king. As with the splinter bid, opener's negative response is to bid 4-trump-suit, otherwise again the most telling positive bid. Opener needs to bear in mind that responder may need this information to judge between small and grand slams.
So which bids are trial bids? If hearts is the intended trump suit and opener super-accepts with 2NT, 3♣ is a trial bid, and 3♥ is a [puppet] trial bid in spades. If responder re-transfers via 3♦, then 4♦ over 3♥ is a trial bid. Note that if responder re-transfers and then bids 4♣, this is a cue-bid [3♣ was available as a trial bid]. If spades is the intended trump suit, 3♣ and 3♦ are both trial bids, and 3♠ is a puppet trial bid in hearts. So in this case, as all three non-trump suits can be trial-bid at the 3-level, re-transferring and then bidding any one at the 4-level is a cue-bid.
Trial bids are a difficult area memory-wise, because they're not going to come up very often. What makes complete sense when everything's fresh in the mind may be a different kettle of fish when it first comes up in 2012!
There's the danger that the super-accept bid is pushing the bidding way too high, but this is a risk that we're prepared to take. Taking the situation where 2-major would have made, but 3-major goes down, we have to bear in mind that any sort of decent opponent is unlikely to let us languish in 2-major in such circumstances, but pushing things to 3-major before the opposition can get their act together is likely to be a good thing. If we occasionally sustain a nasty penalty or adverse score, so be it - it's frequency that matters.