Here's my take on chain compatibility (wrote it down for my own use, has worked for me so far, but use your own common sense and caution).

Briefly put:
Going with a chain for one (or more) speed fewer than the cassette is generally not a good idea.

Going with a one speed plus chain is OK (unless we're talking about some exotic shain design, like the Shimano XTR M9100 12-speed chains - I haven't tested these with a "normal" drivetrain so can't say).

More than one speed plus with a chain?
Well, I'm currently running a 10-speed Ultegra chain on a 7-speed drivetrain. Works fine.
I would expect an 11-speed chain to work OK with a 9-speed cassette.

Would I do it?
No. It's more expensive, with marginal weight savings (my 10-on-7 is an experiment, and since it works fine, no use to throw it away until it's worn).