  We show that if K is a satellite knot which admits a generalized cosmetic
crossing change of order q with |q| \geq 6, then K admits a pattern knot with a
generalized cosmetic crossing change of the same order. As a consequence of
this, we find that any prime satellite knot which admits a pattern knot that is
fibered cannot admit a generalized cosmetic crossing changes of order q with
|q| \geq 6. We also show that if there is any knot admitting a generalized
cosmetic crossing change of order q with |q| \geq 6, then there must be such a
knot which is hyperbolic.
