A lot of people probably already know about the Muppet Stayman solution to Puppet Stayman's inability to handle Responder with 5♠/4♥. Opener bids 3♥ when he has no 4-card or five-card major (instead bidding 3NT with five hearts), to allow Responder to bid 3♠ with 5♠/4♥.
This same restructuring principle (3NT=hearts, 3♥=negative) can be used in other situations, to solve other, similar problems.
A classic problem example would be in formulating defenses to when your 1NT or 2NT opening faces a 3♦ intervention. Playing Responder's double as negative only goes so far. If you treat the double as "Stayman," and have Opener bid 3NT with four hearts, 3♠ with four spades, and 3♥ with no four-card major, then Responder can, again, better handle the hand with 5♠/4♥.
This same structure works if a strong 2♣ opener rebids 3♣. Responder can bid 3♦ as "Stayman," asking about the majors. If Opener does not have a four-card major, he bids 3♥ (3NT would show, again, four hearts), allowing Responder to better handle a hand with 5♠/4♥.
How about after 3♣ interference of a 1NT or 2NT opening. My usual defense is for a double to be Muppet Stayman, with transfers (3♠ showing diamonds). One could, however, decide that ditching transfers and an easy way to show diamonds allows a possible improvement of 3♦ as a modified (as discussed) Stayman bid "with a stopper," making the double of 3♣, Muppet, deny a stopper.
Another instance of this big principle might include the sequence 1♣-3♦-? If the double is negative, inversion of the 3♥/3NT meanings allows Responder to, again, better handle 5♠/4♥.
A more convoluted example carries this even further. Suppose that 2♣...3M shows a four-card major and longer diamonds (Belladonna?). There is still a problem when Opener has 4-3-6-0 or 4-3-5-1 shape if Responder has five hearts. The solution to that problem is to have Opener bid 3♦ with those problem shapes, reserving 3♠ for hands with four spades, five or more diamonds, and less than three hearts. When Opener does bid 3♦, this time Responder, if he is not about to raise diamonds, acts sort of like 3♦ was actually Muppet Stayman. If he has a 5-card major, he bid 3♠ (spades) or 3NT (hearts). If he does not, Responder bids 3♥, allowing Opener to now bid 3♠ if he has that 4-3-6-0 or 4-3-5-1 hand. Note the secondary benefit that Opener declares more of the 3NT contracts this way.
There may be many other instances where this may pay off. A very obscure one to consider is an inversion of 3♥ and 3NT as advances of a takeout double of a 3♦ opening. 3♥, in that situation, could grab onto and also include hands where Advancer might be struggling between a 3NT advance and a 4♣ advance. By putting these into 3♥, you allow Partner to, in a sense, make an insufficient bid of 3NT after your "4♣ call." If he wants you to tell him what you were thinking, he bids 3♠, and you end up at the same spot. The downside is that 3♥ is no longer a possible contract, but strain and not unnecessarily bypassing 3NT might be sufficient compensating benefits.