Do multiple LSAT Argumentative Writing samples help an application?

Hi everyone! I took both the June and September LSATs this year and already have an approved Argumentative Writing sample from June. I'm wondering whether there's any real benefit to submitting another sample after the September test.

I'm actually fine with my initial sample -- while not the best essay ever, it was reasonably coherent and didn't have any glaring issues. I'm mostly asking because I've learned that schools actually do look at writing samples and that there's a possibility they may receive a bit more attention in future cycles, given AI and all.

My hesitation is that, as I understand it, schools can receive up to the three most recent reportable writing samples, so doing another one would technically give them another sample to potentially compare, rather than replacing the first. I just don't want to try again and somehow end up writing something less coherent than my initial sample. If there's a meaningful benefit to doing another one, I'd definitely spend some time brushing up on my timed writing first so I could produce something on par with or better than my last. I'm not applying this cycle, so it wouldn't be taking time away from applications, just time I spend watching shows.

I realize that, in the context of an entire application, this may not matter much at all, but I wanted to see whether anyone has any up-to-date information or admissions expertise on this.

So, would having more than one equally decent—or slightly improved—writing sample be a positive for an application, or is it mostly a waste of time? Likewise, if all your writing samples are fairly run-of-the-mill rather than Pulitzer-level, does it mostly function as a check on basic writing ability and perhaps a way to compare against potentially AI-assisted application essays?

Thank you!