Inspired by your comments, I decided to play around with Celtic knots (as opposed to Celtic braids) this morning. Several hours of experimentation produced this:
Technically it’s 26 shafts (92 treadles if you express it in treadles) but because of the symmetry I am fairly certain it’s reducible to 24 shafts (possibly even fewer!). I wouldn’t be able to sample it on straight draw threading, which is what I’m using for my sample, so I will probably not use this design in the coat.
Nonetheless, it’s very pretty, and I’m going to file it away for future reference. Someday I’ll weave it, or a variant of it, up. (I am still not 100% satisfied with this draft, it seems a little busy to me.)