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I came across the following innovative idea by Angel3D at chess.com:

Slider moves can be generalized by requiring they end in a certain rectangular area, (which could be the entire board), rather than on a ray through the square of origin, with the requirement that the rectangle spanned by their move (i.e. of which the square of origin and the destination are opposite corners) should not contain any pieces (other than the piece itself and a possible capture victim on the destination square). This way, an ordinary slider of range N would be an Nx1 area mover, as the 'area' that must be empty to allow the move is just the (1-wide) ray it moves along. But real area movers have both their ranges larger than 1.

On an empty board such area movers are reminiscent of hook movers (which make the sliding move twice, in perpedicular directions). But they are in fact much weaker (or, to put it in perspective, not as insanely strong), as they can be easily blocked, because the entire rectangle they 'sweep' should be empty, while for a hook mover only the two edges of the rectangle it travels have to be empty.

The idea can be combined with virtually all existing move concepts: you can have diagonal area movers, sweeping 45-degree rotated rectangles (i.e. the 'conjugates' of the orthogonal ones), limited-range area movers characterized by two ranges, area riders based on elementary steps that jump over squares, lame area riders that are even blocked by pieces inside the swept rectangle on squares they cannot not visit, area hoppers, which must leave exactly one piece in the swept area, etc.