I'm not George R. R. Martin or Anne Rice so very few people will be interested in this, but just for the record, I thought it would be good to state my opinion on fan fiction.
Now it would be pretty hypocritical of me to say no to fanfic after being part of over 400 RPG storylines in the past decade. Some was bad writing, some had cool ideas, some was decent writing, and some even had kick ass storylines started from down right evil ideas. Bottom of line, it was a lot of fun. And it wouldn't be right to take that away from my readers.
So, if you want to give one of my characters a backstory or take them on a new adventure, as long as you're not making any money out of it, feel free to do so. Have a blast, I mean it. They gave me a great time, and I want that for you too.
Oddly enough, I'd be less thrilled if you took one of the characters I wrote fan fiction for at some point or another, but for a proper reason. They have already survived going through my hands and being turned into what I needed them for my stories. If you did the same to them, they would become unrecognizable.
Just a bit of a warning: one can develop some really bad habits while writing fan fiction, I know I did. If your only goal is to have fun, by all means go ahead and write. If you want to improve your craft, don't.
Anyway, going back to the main topic, Max seems to have a lot of fans out there, and he deserves a story of his own. :) I'm lost in a different realm at the moment and I'll be stuck there for a while so he won't get it any time soon. If you do decide to write it, you might want to wait until spring when you might get a hint in which direction to go. ;)
I've got only one request: be nice if you play with them. They're people too, you know...