If your PARTNER overcalls 1NT (or 2NT over a Weak Two bid), all systems are on, e.g. Stayman and Jacoby Transfers.
Example #1: LHO (Left-Hand Opponent) opens 1♣. Partner bids 1NT. Right Hand Opponent (RHO) passes. You bid just as if partner had opened 1NT. You ignore the 1♣ bid.
Even if RHO doubles, systems are still on.
If RHO raised to 2♣, double is Stayman and transfers are still on.
Example #2: If LHO bids 2♥ (weak) and partner overcalls 2NT, it is STILL 15-18 with at least one heart stopper. Systems (Stayman/transfers) are still on—just at the three level, so advancer (partner of the overcaller) needs to have 10 or more HCP because bidding is forcing to game. Unusual 2NT does NOT apply over a Weak Two bid—it is much more important to be able to show a hand that otherwise would have opened 1NT, though the range is expanded slightly from 15-17 to 15-18. Nor is 3NT the replacement for the Unusual 2NT bid. 3NT is to play.
Example #3: If Responder bids 1NT, there is no Stayman or transfers. 1♣ by partner; 1NT by you. No Stayman or transfers because NT bidder has already denied four cards in any major. Ditto 1♦-P-1NT. Ditto 1♥-P-1NT (does not have four spades).
Example #4: If Opener rebids 1NT, there is no Stayman or transfers because Responder has already had a chance to bid a major. There is, however, New Minor Forcing (NMF) which Responder can use with invitational HCPs and a 5-card major. So 2♦ in the uncontested sequence, 1♣ 1♠; 1NT 2♦ (*ALERT—NMF) asks Opener if she has three spades or four hearts. Opener shows four hearts first (because 4-4 fit often makes one more trick than 5-3 fit while the converse is uncommon) and shows three spades next time around. Opener also JUMPS one level if she has 14 HCP because Responder has 11 or more HCP to use New Minor Forcing. So, after the above beginning:
2♥ (minimum hand of 12-13) and four hearts (may or may not have three spades) [If Responder next bids 2NT or 3NT, Opener bids spades at the cheapest level to show her three card spade support]
3♥—maximum hand of 14 HCP and four hearts (may or may not have three spades) [If Responder bids 3NT next, denying hearts, Opener bids 4♠ if she has three card spade support. NMF GUARANTEES five cards in the major because otherwise you would just raise partner's NT bid.]
2NT—minimum hand—fewer than four hearts; exactly two spades.
3NT—maximum HCP (14) and fewer than four hearts; exactly two spades.
Example #5: If Opener starts with 1♥ and Responder bids 1♠ and Opener rebids 1NT, NMF still applies. Responder can use 2♣ OR 2♦ to make the New Minor inquiry with five spades and 11 or more HCP. Generally picks whichever minor she has more "stuff" in, either HCP or length.
Example #6: If Responder has a 6-card major, she does NOT need New Minor Forcing. Opener's rebid promised at least two cards in her major. So, responder signs off, invites game, or bids game in her major depending on her HCP strength. [In rare cases, Responder might use NMF with a 6-card major because she has slam interest and wants more information about partner's hand.]
So after the uncontested sequence, 1♣ 1♠; 1NT, responder’s second bids mean:
2♠: six or more spades, no interest in anything more. “Don't write; don't call.”
3♠: six or more spades, about 9 to a bad 12 HCP. Usually 8 losers. "Bid game if you've got good stuff, especially Aces and Kings."
4♠: six or more spades and enough values for game. Usually 7 or fewer losers.
Example #7: Remember 1♠ response followed by 2♥ over Opener's 1NT is the ONLY time a new suit by Responder is NOT FORCING. That shows the weak 5-4 in majors hand and is "pass or correct." NO interest in getting higher. ALL good hands go through New Minor Forcing.
So the sequence 1♣ 1♠; 1NT 2♥ gives Opener only two choices: PASS with four hearts. Go back to 2♠ with fewer than four hearts. Ditto 1♦ 1♠; 1NT 2♥.
If Responder had 11 or more HCP, she would have used NMF.
Hope that clarifies matters.
If you need a copy of the NMF handout, let me know.