Fan fic is allowed, but only under certain rules. I have had to establish some guide lines because I’ve run into trouble in the past, as people put their own spin on my copyrighted characters. I don’t mind that someone wants to continue the story for themselves. But I DO mind when the fan fic writer changes my characters into something they are not, or makes them do things or say things they WOULD NOT DO. Or at least, that they wouldn’t do in public. Personally, I would hope you would not even ask them to do things like that in the privacy of your own head, actually. That would probably mean you have missed the point of the entire book.
But if you can keep yourself from using crass or disrespectful language, and do not ask my characters to break the moral code you can OBVIOUSLY tell underlies their story (sexual or otherwise), or ascribe to them life choices they have NOT made, you have my permission to embroider.