No clue how I'd go about making this work.
Currently I use the online version of FLAG (Fanfiction.net Lightweight Automated Grabber) from
http://flag.erayd.net/ to grab Stories (multiple chapters at a go) from Fanfiction.net and them manually importing them into Calibre.
https://www.mobileread.com/forums/showthread.php?t=26055 has info and downloads on the FLAG program.
What would be ideal, however, would be a custom recipe, based on FLAG that would have an input for the Story ID that could then go about fetching the whole thing (as the stories are split across multiple "chapters" across several pages). Unfortunately, I can't code my way out of a paper sack, and haven't the foggiest idea how to do this sort of thing.