So, now we get to the big idea.
Suppose that two suits have been closed out.
So far, GF, spades agreed.
In this auction, Opener's bypass of 2NT (which would deny two of the top three spades) inferentially promised two of the top three spades. His cue of 3S later showed the third top spade, "closing out" the spade suit. We now know about the Ace, King, and Queen of spades.
Opener's cue of 3C showed one of the top three clubs. Responder's cue of 4C showed the remaining two top clubs. Thus, the side suit clubs is also "closed out."
In this situation, then, the closing out of clubs (one of the two side suits) converts diamond and heart cues to straight control bids.
So, a few things happen, and we know that the reds are covered before someone bids 4NT.
What is that?
Well, at this point, the only unknowns seem to be the nature of the red suit controls. Are these aces or kings? Shortness?
It seems to me that closing out both the trump suit and a side suit should make 4NT a rather precise bid. If the nature of the red controls in this example is unknown, then the responses to 4NT should clarify that issue. To explain, consider the example (black suits closed out, red suit control type unknown). What could be done now?
4NT = please explain red suit control types:
5C = One Ace
5D = No Aces
5H = Two Aces
If the person answering has one Ace and a void in the obvious suit, he bids 5S.
If the person answering has one Ace and a void, but there is no obvious location for that void, then 5S shows the lower void and 5NT shows the higher void.
If the person bids 5C (one Ace), then 5D asks for a possible void. Without a void, sign off at the lowest level. With a void in the obvious suit, cuebid resumes. If the location of the void would not be obvious, show the location of the void by steps (lowest non-signoff shows lowest void; highest non-signoff shows highest void).
If a void is not possible, then 5H+ show two Aces and are immediate cuebid resuming bids (including 5H). In that event, as well, there is no "asking bid" for the void, but cuebidding resumes.
If a triple closeout occurs, if that is possible, then 4NT should simply ask for clarification of the remaining suit. I'll let others come up with those rules, if anyone wants to go that far.