SAYC. 2C, non-forcing Stayman (the bidding can stop in two of a suit), asks opener to reply 2H with four (or five) hearts, otherwise 2S
with four (or five) spades, or 2D with three or fewer cards in each major. Usually responder has 8 HCP or more, but may also use Stayman with a weak 4=4=4=1 hand (singleton club). A new-suit continuation by responder is natural,
promising five: 3H or 3S is forcing to game, 3C or 3D is slammish.2D is a transfer to 2H, and 2H is a transfer to 2S. Each denies exactly four cards in the other major. Opener normally accepts the transfer, but may jump-accept
with 4-card support and 17 HCP. Responder's new-suit rebids are natural and game-forcing (except for a 2D responder's 2S rebid). His same-suit and 2NT rebids invite game. All his notrump rebids offer a choice between notrump and
his major. 2S shows a weak club or diamond hand. Opener must bid 3C. Then responder will pass or correct to 3D (which opener must pass).
Direct 3C and 3D jumps are natural and invitational: opener may pass or bid 3NT. 3H and 3S
jumps are natural and slammish (promising six).
4C is Gerber (ace-asking). Opener replies in code: 4D = 0 or 4, 4H = 1, 4S = 2, 4NT = 3. Responder may rebid 5C to ask for kings using the same code, or place the contract directly
over opener's reply.
SSS. 2C is Stayman, promising at least one 4-card major and asking opener to bid a 4- or 5-card major if he has one (else 2D). With two 4-card majors, opener chooses which to bid first (why not the
stronger?). Responder may be weak with 5-4 in the majors (he'll pass opener's major-suit reply, but bid a 5-card major over a 2D reply) or five diamonds and 4-4 or 4-3 in the majors (he'll pass any reply). Otherwise responder has
game-invitational values or better. A new-suit continuation by responder at the 3-level is natural and forcing.
2D and 2H are transfers. To jump-accept, opener needs 4- or 5-card support in a hand that promotes beyond his normal
maximum for 1NT because of the fit (and usually, a ruffing value).
If transfers are good for majors, letting the strong hand declare and creating many auctions, why not for minors too? 2S is a transfer to 3C, and 3C is a transfer
to 3D. Each may be weak (responder will pass) or game-forcing (responder will bid again, usually probing for 3NT or slam). To "invite" 3NT with a good six-card minor, responder simply bids 3NT: unwarned of the long minor,
the opening leader may make a passive lead that lets declarer romp home with nine fast tricks.
You really don't need 3D, 3H and 3S jumps, so you can leave them idle. However, if you want to use them for something, you might
try these "two-fisted" transfers with a willing partner. 3D shows 5-5 in the majors (game-forcing). 3H shows 5-5 in the minors (game-forcing): opener can bid a minor in which he is willing to play game or slam, bid 3NT to
suggest playing there, or bid 3S to hedge, letting responder decide whether to sign off in 3NT or bid beyond 3NT to seek a minor-suit game or slam. 3S shows a balanced hand with 4-4 or 5-4 in the minors that may produce a
minor-suit slam if opener has a fit and prime values, but not quite strong enough to invite slam by raising to 4NT (opener will usually sign off in 3NT but may bid four of a minor if interested in slam).
No Gerber: 4C is unused.
In 56 years of playing bridge, I've had exactly one hand that was suitable for a Gerber 4C response to 1NT. I was playing high-stakes rubber bridge with a British champion as my partner: he messed up the reply, and played a laydown
7S in 4S. Your partners will use Gerber, if available, on hundreds of unsuitable hands before they get one appropriate hand for it. Why give them a tool they will almost surely misuse? (Partners love to take charge by asking
questions, even when your answers won't tell them what they need to know to make informed slam decisions.)