How there could be 8 books instead of 7 (Spoilers Extended)

Background

GRRM: When I started, my goal was three books. Now I plan to wrap it up in seven books. The story is more involved now, but I have already planned the ending. Yes, I know how it’s going to end. -SSM, Deep Magic Interview: October 2005

While I strongly believe in order to do this series its true justice that GRRM would need 9-10 books, it is worth noting that in addition to already having expanded the number of books numerous times. From an original trilogy to the now 7 books, I thought it would be interesting to point out few times where GRRM has at least wavered on the 7 book number. (and two times (one by GRRM/one by his editor) where they explicitly mention 8 books being a possibility).

Explanation of Expansion of the Series

Originally sold as a trilogy:

When I sold it in 1994, my agent sold a trilogy. But as Tolkien said about “Lord of the Rings,” the tale grew in the telling. So I got back to writing it, and I’m writing it and writing it, and pretty soon I have 1300 pages for the first book and I’m not anywhere near close to the end. -SSM, NY Times Interview: April 2011

It then moved to 4 and then 6 books:

So at that point, I said, “Ah, maybe it needs to be four books instead of three.” And then at some point I said, “Maybe there needs to be six books instead of four.” I skipped right over five. And then for several years on book tours, I would say, “Yes, there are going to be six books.” And my girlfriend at the time, now my wife, Parris, would be standing behind me and she would hold up seven fingers. [laughs] -SSM, NY Times Interview: April 2011

Seven Books for Seven Kingdoms

He then decided on 7 books:

Finally I acknowledged that she was right. Seven books is good. Seven kingdoms, seven gods, seven books. It has a certain elegance to it. So that’s my story now and I’m sticking to it.
Q. I’m sure your agent was thrilled that the series kept growing longer. But what about your publisher?
GRRM: My publisher is quite excited, as long as I don’t take 10 years to write each of the books. That part, they’re not too excited about. They would like me to write a little faster. Thankfully they are patient and they wait for me. -SSM, NY Times Interview: April 2011

before wavering again a few months later (note that he finished a couple incomplete ADWD/move a few chapters to TWoW at this time)

Q: So how firm are you that Ice and Fire will be seven books?
GRRM: I’m as firm as I am, until I decide not to be firm. -SSM, EW Interview: 12 July 2011

8 Books for 7 Kingdoms?

On the surface it doesn't makes sense:

“My sweet sister has arranged the feast. Even if I could secure you this invitation, it might look queer. Seven kingdoms, seven vows, seven challenges, seventy-seven dishes … but eight singers? What would the High Septon think?” -ASOS, Tyrion IV

But back in 2014, GRRM's publisher Anne Groell stated this:

Q: Do you think it will take GRRM more then 7 books to finish ASOIAF?
Anne: I begin to wonder—though 7 is what we currently have under contract. I remember when he called me, years and years back, to confess that his little trilogy was…well…no longer a trilogy. He predicted four books. I said Seven Books for Seven Kingdoms. Then he said five books. I said Seven Books for Seven Kingdoms. Then he went to six. I said… Well, you get it. Finally, we were on the same page. Seven Books for Seven Kingdoms. Good. Only, as I recently learned while editing THE WORLD OF ICE AND FIRE (another awesome thing you must buy when it comes out!), there are really technically eight kingdoms, all having to do with who has annexed what when Aegon the Conqueror landed in Westeros. So, maybe eight books for Seven Kingdoms would be okay. Also, he has promised me that, when he finally wraps this great beast us, I can publish the five page letter outlining the bare bones of the “trilogy.” -Anne Groell Interview: June 2014

and this might be the quote that she is referencing (its from Fire & Blood technically):

The Westeros that Aegon the Conqueror had found had consisted of seven kingdoms in truth and not just name, each with its own laws, customs, and traditions. Even within those kingdoms, there had been considerable variance from place to place. As Lord Massey would write, “Before there were seven kingdoms, there were eight. Before that nine, then ten or twelve or thirty, and back and back. We speak of the Hundred Kingdoms of the Heroes, when there were actually ninety-seven at one time, one hundred thirty-two at another, and so on, the number forever changing as wars were lost and won and sons followed fathers.”

or this one from TWOIAF that references seven (Islands/Rivers were one kingdom at the time):

The Westeros of Aegon's youth was divided into seven quarrelsome kingdoms, and there was hardly a time when two or three of these kingdoms were not at war with one another. The vast, cold, stony North was ruled by the Starks of Winterfell. In the deserts of Dorne, the Martell princes held sway. The gold-rich westerlands were ruled by the Lannisters of Casterly Rock, the fertile Reach by the Gardeners of Highgarden. The Vale, the Fingers, and the Mountains of the Moon belonged to House Arryn...but the most belligerent kings of Aegon's time were the two whose realms lay closest to Dragonstone, Harren the Black and Argilac the Arrogant.

its just worth noting that there are 8 not 7.

GRRM Mentioning 8 Due to Sizing

On the Game of Owns Podcast in 2022 GRRM mentioned how the size of TWoW (its going to be a massive book) could cause it to be split into two volumes (a notion he was previously resisting from a stopping point standpoint not a size standpoint):

GRRM: It was a trilogy. And then it became a four book trilogy. Gene would joke about it, yes my four book trilogy. and now I have my seven book trilogy, if I can indeed finish it in seven books, but there it is.
Speaker 3: I was Just gonna say, we love the addition additions to the trilogy. So keep adding them. And on in that energy, do you think that it might go beyond seven? Could you go beyond seven books?
GRRM: Well, in a sense, it already has, with Dunk and Egg and Fire and Blood and all that.
...
GRRM[Regarding the main series]: I hope not. I hope not. I mean, honestly these are big books. It is conceivable, and I do not know, this is not a definite answer, okay? But that...Winds of winter might be a bigger book than either Storm of Swords or Dance with Dragons, which are the two biggest books. And I'm not talking 10 pages bigger, I'm talking 300 pages bigger or something like that. Now, if that happens, my publisher might want to divide it into two books. So in that sense, it's already gone beyond seven. They might say, "this is too long. We can't fit it. So your choice is to cut it." you know, go through and trim it and tighten it down, lose 300 pages, or to divided into multiple books. And then I will have to wrestle with that situation when it comes up. But first I have to finish it and see exactly how long it is. And is there any place to divide it? Does the publisher wanna divide it or they wanna publish it? I may have different, you know, it has happened before, that my American publisher decides to go one way and my British publisher decides to go another way. And then, you know, you get into situations like in other countries, like France, Italy, where they divided into six books.
Speaker 2: Well for the publishers out there, we'll read a 1500 page hard copy. Yeah, no problem. yeah. We'll read a 1900 page hard copy. Yeah. If they split it, would they, would they call it two different things or would it just be the winds of winter part one and two?
GRRM: I would then be discussed. I mean, you can split it into two books, but you can release it as one, you can have two volumes in a slip case. Or something like that. and then you, then you do call it winds of winter one, winds of winter two, or you give the second part a different title and you don't publish it simultaneously. You publish it six months later or a year later. And et cetera, you know, this is the situation. I mean, this is not a new situation. This is a situation I faced with a dance with dragons. I mean the fourth book was supposed to be a dance with dragons. -SSM, Game of Owns Podcast: July 2022

TLDR: Both GRRM's then gf (and now wife) Parris and publisher (Anne Groell) had advocated for "Seven Books for Seven Kingdoms" while GRRM was still sticking to 4 and 6 books. He obviously relented on that as that is now what is currently forecasted for the series. Since that time, GRRM has considered moving to 8 books (due to sizing, not plot cutoff) which his publisher states wouldn't be an issue since technically there are 8 kingdoms.