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An extension that might also be considered is the use of [gain-type] or
[loss-type]. Up to this point, the discussion has focused on adding or
subtracting the power to move or capture, but the relayed power added or
subtracted might be movement to a vacant space, movement to an
opponent-occupied space, movement to a vacant or opponent-occupied space,
etc..
(the possibilities might also include interchange powers -- the right to
switch places with a friendly piece).

I would also consider a piece observed by or a piece observing as only two
options in defining the 'source'. A relay-type relationship might also
be triggered by an absolute relationship (e.g., piece a K-move away,
N-move away, B-move away, etc.) -- essentially the [gain-condition] or
[loss-condition] could be defined by any rule that, when applied to a
potential source, temporarily evaluates to true. 

Obviously we don't have to use all the facets of 'generalized relay
chess' to define a CV in the family. A broader framework does allow some
curious family members.

A simple example might be called 'Channel Chess' -- Any RNBQ may move to
a vacant space with the movement power of the last friendly piece
captured.