To clarify, what is the chess-board configuration that would maximize the number of valid moves one player could make on his or her turn? I thought of this question while playing chess, how apropos. I doubt there is a unique configuration, but I am not sure. The problem seems difficult because one must consider every single piece's movement, and the limitations on that piece's movement by other pieces. At any rate, I appreciate any thoughts, hints, or solutions.
If just the major white pieces are placed on the board, there is an almost-unique 100 move solution. There are many variations, and a couple of dozen of them are given in Guide to Fairy Chess by Anthony Dickins. Some of these are also given in Martin Gardner's Sixth book.
These are known as construction tasks.