Is a "three under" approach possible and sensible as a means of including and asking bid? Sure. The situation would be one where Overcaller makes or doubles a three-under call, with room for Advancer to use the two-under call as an asking bid or relay on weak hands, other calls being invitational.
Consider your problem if the opponents open 2NT as a light opening, both minors. This is a tough situation to defend, and I have thought long about the most effective defense structure to that opening. Well, what about incorporating a two-under and a three-under plus asking approach?
Overcaller could bid 3D for both majors, values, or 3M with that major and values. Advancer moves accordingly. So far, rather normal.
We then add the two-under for Overcaller, who is light. 3C shows a lighter overcall with one or both majors. If Advancer has spade preference, he bids 3D, which allows some unwind and a decision from Advancer. With heart preference, 3H is the call, or 3S as a "paradox" call (I have interest in a heart game but not a spade game if you just have long spades). 4C would be the game-force unwind.
Next, consider the double of 2NT, a "three-under plus asking" double. This shows a takeout hand, but the majors might be of different lengths (4-4, 4-5, 5-4, 4-3, or 3-4, or even 3-5 or 5-3 are possible).
Advancer, hearing this double, could bid 3M as an invitational call, agreeing the indicated major with tweener values -- he needs extras for game to be a good bet. With equal majors and game interest, Advancer bids 3D after the double, asking doubler to pick the strain and level.
If Advancer has a weak hand and wants to get out at three of one of the majors, he bids 3C, a Herbert Negative asking bid. Advancer has either a specific major he wants to play at the three-level OR a weak hand with equal majors, wanting to play the right major at the three-level. Doubler bids 3H with longer of better hearts, 3D with longer or better spades. After either, Advancer places the contract.
A similar approach could be used to compete over Flannery. One could play that a three-under 2H cue of a Flannery 2D opening shows both minors. If this were used, Advancer could bid 2S as a Herbert-negative two-under signoff, allowing the 2H cuebidder to pick his longest/best minor (2NT with longer/better clubs), to make sure that the contract ends up being the best minor fit if Advancer has equal minors. The 2Nt call allows room, again, for Advancer to bid the Herbert Negative with the asking bid tool while maintaining the ability to get out at 3C. If Advancer has game interest, he could bid three of his preferred minor, showing extras.
How about after a Roman 2S opening, showing clubs and spades? Three-under for the reds is a double. If 2NT is then Lebensohl-style, you end up in the same scheme. After 2NT, doubler can bid 3C to show better/longer hearts, and the weak hands end up played in the right strain.
In summary, the three-under plus asking bids is a way to have the person bidding (or doubling) a call that is three-under his two known suits, with Advancer using a counter two-under call as a weak relay with an added asking-bid included safely, to enable other calls to have values attached.
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