[vitus]

> A maximum of 8 pawns (4 white and 4 black, for example) can possibly be advanced over the course of the game to the opposite side (6 squares ahead from their home square).

Not so! Pawns move diagonally via capturing, which theoretically could allow white to promote all 8 pawns just in the d column, and black to promote all 8 in the e column (at the expense of various other pieces).

edit: of course, you'd run out of pieces first, but you can accomplish something similar by using multiple columns.

Sample game start that accomplishes a subset of this (2 pawns promoted from each side, 6 pawns remaining from each side):

1. Nf3 Nc6 2. Ng5 Nb4 3. Ne6 Nd3+ 4. exd3 dxe6 5. Ke2 Qd7 6. Kf3 Qc6+ 7. Kg3 e5 8. d4 e4 9. d5 e3 10. d6 e6 11. d7+ Ke7 12. d4 Kf6 13. d8=R e2 14. Rd5 e1=R 15. Ra5 Re5 16. d5 Rh5 17. d6 e5 18. d7 e4 19. d8=R e3 20. Rdd5 e2 21. Rdb5 e1=R

https://lichess.org/wtJoIdT3#42