Efforts are underway to redefine the kilogram as a precise number of atoms of a solid, for example, a silicon sphere of a known volume.
Consider a vaguely similar approach but with a liquid. Create a vessel whose volume is very precisely measured, perhaps with laser scanning, the same tool used to measure the sphericity of the aforementioned solid. Fill the vessel with a liquid. Measure the meniscus effect of the surface again with laser scanning.
Cryogenic hydrogen might be a good liquid, as hydrogen-1 and deuterium can presumably be easily distinguished and separated due to their vastly different masses. One of the superfluid heliums might also be a good liquid with their tendency to completely fill a vessel leaving no voids. However, self siphoning might be annoying.
Presumably this has already been considered and rejected. I'm guessing the dependence of volume on temperature and pressure make it too difficult to precisely replicate.
In zero gravity, no vessel is required.
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