Kinda
The problem is that you have to either divest identifiable parts of the original, and do so in a way that's so severe it essentially becomes something other than fanfic; or you have to be doing custom writing on commission.
You aren't going to get many commissions for standard fanfic though, so I hope you're good at erotica.
Sadly, the market for that collapsed hard about fifteen years ago, and the prices dropped you insulting levels as well.
Regular fanfic, at best you'd get a trickle. Erotica, believe it or not, used to be a niche for not just fanfic, but in general for writers willing to do a one-off. The problem was/is that it's a one time sale, no royalties. You do the job, hand it over, collect the final part of the pay, and that's it.
Unlike regular fanfic, the erotica fanfic, you could charge serious bucks because it was a seller's market.
Like, typically, if you're getting 50 cents a word for your custom writing, you're doing very well indeed. On average, you're looking at under half that. But custom erotica? A dollar plus per word was not rare. At one point, I wouldn't waste my time for anything under that, it just wasn't worth my time, even if all they wanted was something quick and easy.
You get a request for something novella length, and you're looking at some decent chunks of change, with the right customer. You gotta think, a novel can be maybe 50k words at the low end. Novellas are less than half that, but still over 15k words.
You have to back off on your per word rate with bigger stuff like that, but $10,000 for a decent length, multi chapter story happened back then. You get a customer that really likes your work, and you might get requests for that level of thing yearly, or twice a year, with requests for shorter work thrown in between. The car I have now, I bought off the sale of one of the longer pieces I did, but it wasn't fanfic.
But nowadays? You aren't getting that. Nowhere close. There's too much free out there, even if the quality is lower than you'd get with someone that's practiced at the craft. Last time I got a request, it would have come out to five cents a word, and that's a fucking joke. Not worth the time and effort, even for a short story a few pages long.
You might be able to set up on patreon and get a trickle going though. I don't personally know anyone making a living that way, but it apparently can be enough to be worth doing in your spare time, if you'd be writing anyway.