Maximum number of white queens and black knights

In another forum, when the topic of the number of possible legal chess positions came up, I commented that this number is heavily increased by the fact that pawns can promote. I commented: "In theory you could have 9 white queens and 10 black knights on the board."

But then, after thinking about it for half a minute I realized that's not true. It's not possible to reach a position with that many white queens and black knights because there aren't enough other pieces for the pawns to capture in order to get past each other.

So that got me thinking: What is the maximum number of white queens and black knights that could be simultaneously on the board (assuming we start from the standard starting position and follow the rules of chess strictly)?

I would have thought this would be an interesting puzzle, but apparently not.

Starting from the standard starting position, all 8 files would be blocked by opposing pawns.

But now consider a blockade like this:

The white b pawn capturing to a file would unblock both b pawns - white b pawn would be leaving the a file blockade behind, and black b pawn is now unblocked.

Does this mean that just 8 captures are needed to unblock and promote all 16 pawns, simply requiring that the pawns capture when past the blockade on the destination file?

The problem is that there are no 8 other pieces of the opposing color for the pawns to capture. That's why not all 16 pawns can promote.

All 16 pawns likely can promote because the newly promoted pawns can get taken by enemy pawns so the enemy pawns can promote

Not a problem because you don´t need 8 pieces of the opposing colour. Capturing the black rook in the example unblocks both white and black b pawns. There is no need to spend another black piece to unblock the a pawns - after the black b pawn has passed b2 (and knighted) get some white piece at b2 to be captured by black a pawn and unblock both a pawns.

You need 8 pieces to capture between both sides combined. And you have them.

It seems that you are right. I tried to get the 9 white queens and 10 black knights, and I was successful. (It's not the shortest possible way of getting them, but it demonstrates that it's possible.)