Wow is this getting interesting to me. OK, the challenge now is to find a common situation where a three-under call (sort of) is enhanced by the theory of three-under bidding. A simple one is a redouble of One Spade!
To escape effectively, the three-under approach for three suits can be used. The redouble makes 2S "three under" the three suits shown by the double, in the sense that it adds pass as the additional level.
If escaping Advancer has one or both minors and wants to play at two of a minor, perhaps two of the right minor if he has both equal minors, he passes. Doubler then picks his minor of preference, bidding 1NT to show preference for diamonds, to allow this move by Advancer safely with either one minor or both minors.
This enables 2C or 2D to show, instead of just that minor, equal length with that minor and hearts.
With just hearts, Advancer bids 2H.
1NT by Advancer, then, could be used to show a desire to play 1NT.
Alternatively, 1NT could show hearts and an equal-length minor with a weak hand, scrambling-style, with 2C or 2D then showing the same pattern but enough stuff that the redouble does not negate game prospects.
This same basic structure could be used after 2S-X-XX, of course.