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Reverse response after initial 1NT

In responding to opener's reverse we want to distinguish between weak and game forcing or better hands, and determine whether stoppers are present for play in notrump.  After an initial suit response, responder can show game forcing or better support immediately, rebid a major with wide-ranging values and not support for opener, bid notrump intentionally with a stop in the 4th suit and no support, and use 4th suit below 2NT or a super ambiguous major rebid as a negative.  That seems to be a common expert agreement with some playing that a raise is game going only, a major rebid is dual purpose (natural or negative) and 4th suit either above or below 2NT is some slamming hand.  That much seems good.  I do not believe there is consensus on these agreements so it's necessary to discuss in each partnership.

Things are different when responder's first bid was 1NT.  Responder's hand is more constrained, some aspects of support are known, and notrump siding is already determined.  There is one odd-ball case, 1-1NT; 2What do responder's bids mean after opener reverses over your initial 1NT response?  Answers may vary depending on other agreements, such as what an initial jump shift would have meant and nuances such as notrump ranges over 1 vs 1 or how you handle weak major suit raises.  Since in all cases responder will have denied a major suit, opener's reverse into a major will show 5+-c (or be a fake reverse with some minor single suiter), responder will raise on 3-c support.  Interestingly, although there are six cases where responder bids 1NT and opener reverses, the four reverse cases where responder starts with a suit get a lot more discussion.

Here are responses that feel about right to me:

2NT is non-forcing, a preference to opener's minor is constructive [should it be forcing?], a raise of diamonds is forcing, 3 after an initial 1 opening is weak (4 shows 3-c LR and jump shift to 4m would show shortness w 3-c LR), 3 of a new minor would be natural and constructive or weak depending on what an initial jump shift to the minor would have been, a new major suit would show a concentration of values (probably denying values in the other major), 3NT would show a maximum in context.  

Thanks.

As stated above.
As above with some additions.
Something different as detailed in comments.

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