That looks like an American Standard brand of faucet. Probably same stem as a Hampton (pic below) or Williamsburg style faucet. The part number for that cartidge might be 994053-0070A pictured below. The cheaper version would be Danco 10472 4Z-24H/C Stem for American Standard Faucet. You should try to call American Standard (800 442 1902), and you should try to send them your pictures (above). And read the fine print on the warranty from American Standard.
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Have to replace a hot water cartridge on an old, unmarked faucet. I can’t seem to find at local hardware stores. It has 33 teeth and is about 2.5”. Anyone able to ID?
That looks like an American Standard brand of faucet. Probably same stem as a Hampton (pic below) or Williamsburg style faucet. The part number for that cartidge might be 994053-0070A pictured below. The cheaper version would be Danco 10472 4Z-24H/C Stem for American Standard Faucet. You should try to call American Standard (800 442 1902), and you should try to send them your pictures (above). And read the fine print on the warranty from American Standard.
It sounds like you've done very thorough footwork & exhausted the market, great job on really trying. I also don't see much of anything that you could rebuild or tighten up.
However, if the plastic can be removed without damaging it. Then, you may find that some items can be removed & replaced by the same pieces from a cheap improper & unrelated replacement, which just has the same diameter.
Conversely, go for "the" or "a" new faucet that fits into your future plan. The primary new faucet consideration being that it comes with an optional deck plate to cover the vanity top's holes.
This is what I've done in preparation for my new bath, where I want a single handle & single hole faucet. I found that many single hole faucets include an optional deck plate, which can be omitted later with the reinstall on the new vanity top.
Call community home supply in Chicago. It’s a Fluhs 16 or 18 point ceramic cartridge. I’m sure a Newport brass cartridge or something similar will be correct. If not, they’ll be able to ID it from a picture.
I don't know the manufacturer. =It is my experience that one can take the all parts to a nearby plumbing supply store (as opposed to Home Depot or Lowes etc...) and the counter people will be able to identify it and provide parts.
There is also an online stem finder tool with an option for unknown manufacturer:
https://www.danco.com/stem-finder/
Another approach I used successfully is to take a couple of photos from various angles of the cartirdge and of the set, then use google image search to find similar photos online. Scan through the results to find true matches. They may have been posted by a plumbing supply house or by a DIY blogger fixing theirs. Lastly if it is just the o-ring, replace the oring as a generic item.