A troubling sequence is anything that starts with a 2NT opening, or 2C...2NT. Space is limited.
I kind of liked my wife's call the other day, as an aside. Bust with 4162. I opened 2C, and she bid an immediate 2H double neg. After 2NT, she whipped out Stayman, figuring that two of three rebids by me would be fabulous and that she could live with the fourth, rebidding 4D. As it was, I passed (I was looking at long clubs for my 2NT call), which yielded an unexpected fourth good option.
But, I am wandering off point. What this dal made me think about was what I might call a "Super Non-Accept." If partner had shown a positive response (2C-P-2D), and then I bid 2NT, it seems like there is something to be said for dedicating one call for great hands without a fit after a transfer.
for example, suppose she transfers to hearts, but I am looking at Ax or Kx in hearts. This is already a great holding if she is two-suited. Maybe 5-4 with a hand where she might be planning on a signoff if I cannot support her major, or even a 4NT quantitative (which burns space). In that second suit, if we have a fit, we have the likelihood of establishing her hearts via ruffing. So, suppose that the first non-relay shows a power non-raise:
Partner could always back into 3NT or 4H (via re-transfer). But, this gives space and incentive to explore alternative strains if she was interested in slam but only mildly (might have bid 3NT earlier). It saves space by not forcing 4NT quantitative if that's what she had. And, it describes. She could trot out new suits by bidding 4C (natural) or 4H (4D is a re-transfer, so 4H shows diamonds).
Now, the 5H/4S for partner scenario can be "fixed" by way of not bidding this 3S call unless you also lack four spades. So, this call would typically show 3244 or a 5+ minor. But, I could live with that.
This obviously might not be the best structure, and there might be something better. But, it seems like there is good cause for that "Super Non-Accept" to possibly be considered.