Many thanks goes to @Retudin in a comment on my last question for this idea.
In a chess position, pieces can be restricted as to how many moves they can legally make in theory. Since my previous question covered n=1, it is time for n=2!
Every single piece, up to 32 in total, may be used.
A position in which as many of them as possible have exactly two legal moves.
In the likely advent of a tie, the position containing the shortest proof game wins.