Without hesitation, I have turned them down. Changing your image is far more difficult than surrendering to it. The kind of madness that accompanies notoriety of this magnitude is like lightening striking. It is unlikely to hit the same individual twice. Diane Von Furstenberg might get famous twice for the wrap dress, but the scarves and luggage she designed never really caught on.
Fame is profoundly cautious.
It has a repetition compulsion. Look what happens to actors who refuse to be typecast. They often can't get work. It's hard for the villain to become the romantic leading man. Tom Berenger will never change places with Tom Cruise.