Is it possible for the (23-year old) daughter of a parent possessing a work permit here to get a longer stay visa? Like, a non-O or something?

I would have her take a copy of your passport/work permit and give it a try putting visit family as reason for wanting a multi entry non immigrant O visa. Am sure the home country Consulates that normally issue to visit friends would issue but you may be able to take advantage of the 'family' word to get a regular Consulate to issue. You could call some of the Consulates to confirm.

If she is interested in schooling that might be another option to consider.

It might help if you can tell us in which country your daughter lives,

then we may be able to recommend a suitable consulate.

She's not my daughter, she's my fiancee

She is a Russian citizen and her father has a small business here and a work permit...she's already here on a tourist visa, any idea if the change can be done in a nearby country, or would she have to go back to Russia to get a Non-O? I also have a work permit, but I think it would be more useful to get a visa through her father, not sure if Thailand has the concept of a "fiancee visa".

Schooling (an MBA here) is an option, but a rather expensive one, which we'd rather not pursue right now...later, yes, but for now she needs a proper visa to get past the 90-day / 6 months stay limit.