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I have been considering a truncated planar piece. One that performs an
orthogonal planar move but only up to a 4x4 area.

For those that are unfamiliar with planar moves, this is basicly an area
leap with the condtion that there are no other occupied cells within that
particular area(excluding the piece which is moving and its potential
target cell).

A classic Knight leap is a 2x3 area leap without the restriction of
occupancy for its particular group of cells.

The planar move offers a piece which can by itself easily checkmate the
common King. So it might only be obtained through promotion, or in games
which utilize a stronger King(such as the Emperor).