[delxzyad] Flying piece

Consider a fairy chess piece with the ability to fly. Instead of unlimited flight to any other square (like the Emperor in Maka dai dai shogi), we restrict its flight in the following ways.

In order to move at all, the piece must be guarded by at least one friendly piece.  It may then fly to any square that that guarding friendly piece can move to (or capture).

Probably avoid applying the rule recursively (the piece guarding a flying piece is another flying piece), though that might make for a good puzzle.

If we allow multiple occupancy on a square, we can weaken the piece further: on the first move, a flying piece may be pulled back to the square of the guarding piece, and on a subsequent move, the flying piece may be launched to wherever the other piece could have moved.