Grand slam bidding with high card points hand
As explanation of why it is completely insufficient to ask "What is my opening bid with a 24 high card point hand ...?" consider these examples of hands with 24 HCP:

QJT9876 AK AK AK     Open 5S, asking partner to pass or raise to 6 or 7 
                     with respectively 0, 1, or 2 controls in the Spade
                     suit. This is a useful asking bid because it is
                     pointless as an opening pre-empt - the only player
                     at the table you are pre-empting by opening 5 of a
                     major is partner.

AKQTx x AKQTx AQ     Open 1S in order to preserve room to show your strong
                     two suiter with a second round jump to 3D. Opening 2C
                     with strong two-suiters is a bad practice, because you
                     will either lose the second suit, or be forced to
                     introduce it at the 4 level where partner will mis-
                     read it as a control bid in support of his suit.

AKxx Kx AQJx AQJ     Open 2C planning to rebid 2NT.

K32 AK AK32 AK32     I lean towards opening 2C planning to rebid 2NT, but I
                     could forgive a partner who simply opened this 2NT.
                     Game is very unlikely if partner cannot move over 2NT,
                     because of the major suit shortness and the poor
                     texture in all suits. 

AKQJTxx AKQ KQ 2     Open 4NT, Blackwood. The only information you require
                     from partner is how many Aces he has, and you may lose
                     the opportunity to ask if you let opponents into the
                     auction.


Update

Consider the following deal, consistent with OP's description. As the hand given by OP is actually 27 HCP, and an obvious 2S opener in consequence, let's amend to be an interesting question, dropping the SK to become:  

S_AQJxx
H-AKx
D_Ax
C-KQJ


opposite something like  

S-Kxx
H-JTxx
D-Kxx
C-Axx


Theoretical issues now aside, and with an actual hand to analyze, let's assume a casual partnership playing a Goren style bidding system - so no relevant conventions beyond Stayman; Strong 2C with a 2D waiting response and a second negative; straight Blackwood; and Gerber as an immediate jump over NT.

Opener has 24 HCP plus a strong 5-card Spade suit, counting 5.5 QT and 9 PT (playing tricks); this is well above the minimum for a strong 2C opener and, significantly, too strong for a 22-24 HCP Strong 2NY opener. Opener should open 2C (or 2S if that is a strong opener rather than a weak 2).

Over 2C responder will bid 2D (waiting) because she is too strong to bid a 2NT response.  Opener rebids 2S to show the strong 5 card suit; and responder rebids 3S (game forcing because a fit has been announced and a 3C second negative wasn't bid). Even if Responder errs and jumps to 4S, which should be a minimum distributional raise in Spades, the partnership should easily find the small slam in either Spades or Notrump. 

Note that the grand, although possibly making on this hand, is a bad bet to bid because it requires responder to have either 4 clubs or for a beneficial break in hearts, or for a squeeze to come home.  This reflects the flaw in Opener's hand of no small diamond, wasting the DJ unless Responder has precisely Axxx or longer. 

To directly answer the question in regards the actual bidding sequence at the table: once Opener underbids with an opening of 2NT and hides the strong Spade suit on the second round, Responder can be forgiven for passing 3NT. There is really nowhere for Responder to go with confidence.