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The Emperor is non-autopositional variable piece, moving to any square
defended by a friendly piece.

The counter of the Emperor would be the Anarchist, which moves to any
square attacked by an enemy piece. Anarchists would make for much more
aggressive games by discouraging defense. The fluidity would be too high
for most initial positions, so there could instead be Libertarians, moving
to any square attacked by two enemy pieces.

Between an Emperor and an Anarchist would be a Moderator, which moves to
any square both defended and attacked.

Pieces of this sort make for careful positioning, and are best suited for
sparse boards.