2. ... Nc6 KIA

3.d4 transposes to a queen's pawn opening. It is no longer a KIA. 

  <--- KIA setup

Thanks for your comment, wormrose. Could you post a game which shows how you would meet 2. ... Nc6? Thanks.

In fact - it was never a KIA. 

1.Nf3 is classified as a Reti by ECO. But this can be misleading, it is not so unless the moves that follow are Reti moves.

  <--- Typical Reti formation

Many believe 1.Nf3 should be classified as a Zukertort, because Zukertort sometimes played 1.Nf3. But he would usually transpose into the popular openings of his day. He did not develop a deep system of play based on 1.Nf3.

Richard Reti did devise a deep system of play based on 1.Nf3 with c4 in which the center pawns are held back during the setup and center control is accomplished from the flanks by pieces (double fianchetto), no piece or pawn is advanced beyond the 3rd rank except the c-pawn. It is not unusual for a Reti game to end with the e-pawn still on e2.

ECO classifies the KIA as a "special case" of the Reti because e4 is played instead of c4 as part of the setup, whereas in a pure Reti the e-pawn would be held back.

In many cases White's development can evolve either into a KIA or a Reti depending on whether c4 or e4 is played.

I will look for a game. But in general, when Black responds with the early ...Nc6 it is an indication that ...e5 will soon follow if it has not already been played. This has a tendency to evolve into a reversed Modern Defense or a reversed Pirc, not exactly a KIA. 

Aha! I remember now:

This is not covered by most KIA books but here are three games from  Hall and Cartier

        The "Modern" KIA
G128  Rivas Pastor vs Illescas Cordoba
G129  Todorcevic vs Illescas Cordoba
G130  Gufeld vs Hodgson

and here from chapter 8 of Dunnington's book "The Ultimate KIA"

https://www.chess.com/clubs/forum/view/kia-dunn2-g8-4

wormrose, you are the man! Thanks for these informative posts.

Sticking to the hypermodern spirit of the KIA, I gladly allow Black to play ...e5 by playing d3 instead of d4, after which I usually undermine Black's center by playing c4 instead of e4 with easy patterns whether Black pushes its d-pawn, exchanges ...dxc4 or keeps developping. At that point it's more an English-like setup, advocated in some cases in the KIA by GM Dzindzichashvili, more than strictly the common KIA setup.

Having "easy patterns" does not mean it's "won" for White in the opening, just that it is not difficult to find a plan until the middlegame (usually by making good use of the light-squared diagonal and a semi-open c or b-file, hitting on Black's queenside).

For instance:

@Wormrose, the KIA is sometimes also called "Barcza system" as on its wikipedia page while the Barcza system refers to Nf3 and g3 played in whatever order as first moves. Fianchetto openings are so flexible, it's often a nightmare to put a name on them, especially "systems" -_- , and it happens that the concrete border to distinguish them is sometimes just a matter of chosen strategy.

Yes, opening nomenclature can be misleading. Probably the most misunderstood opening (in terms of definition) is the Reti; about which there is a great deal of confusion. 

The game you have posted above is a reversed Classical Pirc.

Thanks for pointing it out, I remembered that the same ideas apply in a strict reversed-Benoni position as well as in a position with the pawn in c7 but while typing it, I did not realised it was a Pirc with a tempo up, indeed.

What is nice (at least for me) in playing c4 instead of e4 in opening positions where Black succeeded in pushing e5 is that it gives White clear targets and easy development moves to find without learning a bunch of theory.

 considering one of the main ideas of the Reti opening is to not reveal the specific opening you are playing on the first turn (as it can transpose in to many other systems), it seems understandable that there would be much confusion regarding it.

In the 1920s the Reti was not only a new opening but a whole new way of playing chess. Today the Reti is considered to be 1.Nf3 d5 2.c4. After that there are many possibilities to transpose into other openings and some lines overlap, such as the English Agincourt.

The KIA belongs to the Reti family by virtue of the Nf3 and the k-side fianchetto and the holding back (initially) of the d-pawn. It is considered a "special case" of the Reti due to the move e4 which would not be played in a proper Reti.

When the KIA player is developing a 1.Nf3 KIA, it is technically NOT a KIA until e4 is played since it could easily be a Reti if c4 was played instead of e4.

Wormrose, thanks again for your edifying posts.