[biggerclub]

Logically this seems like the right treatment, but I am always afraid to just spring it on my partners without previous discussion:

(P) - 1♥ - (P) - 2♦
(P) - 2♠ - (P) - 3NT
(P) - 4♦- (P) . . . .

or (leaving out the OPPs' passes this time):

1♣ 1♠
1NT 2♦
2♠ 3♣
3NT (or 3 ♥) 4♣ . . .

Logically these and similar auctions seem like minor suit slam tries and 4NT should reject the try and suggest a contract, not ask for Aces. Still, without prior discussion . . . .

[Zelandakh]

Taking 3NT out into 4m is almost always a slam try (exceptions tend to be obvious). How one proceeds thereafter is a matter of agreement. For example, it would be perfectly logical to use 4♦ as the negative on auction 2 rather than 4NT.

Auction 1 is trickier to comment on as you have not told us the system nor whether 2♦ promises 5 or not. If 4♦ agrees diamonds then it is logical (to me) for 4♥ to be a negative. If 4♦ is merely patterning out then we probably need 4NT for this and 5♣ becomes Last Train. It is also relevant what 4♣ instead of 4♦ would have been.