They found the mutation that causes the salmiak pattern shown above, it's a deletion downstream of the KIT gene (KIT controls several other, but not all, of the other white cat markings). It's a recessive mutation, Photo c in the figure below shows a normal patterned carrier next to his salmiak patterned brother. The carriers may have some white on their coat, but it's unclear if it is due to the single salmiak allele or another cause.
So yeah, it's possible. I'm not aware of any breeding projects for it though.
"FIGURE 1 ... (a) Salmiak solid black cat (aa/wsalwsal), (b) salmiak solid blue cat (diluted black, aa/dd/wsalwsal), (c) salmiak brown mackerel tabby (wsalwsal) (right) and his normal-colored brother heterozygous for salmiak (wsalw), (d) salmiak phenotype on a long-haired solid black cat (not genotyped), (e) salmiak solid black cat (aa/wsalwsal) and (f) salmiak phenotype on a tortoiseshell cat (not genotyped). Cat a was sequenced, and cats b, c and e were genotyped for salmiak. Photo credits: (a) Ari Kankainen and (b–e) courtesy of the cat owners."
Source: A new Finnish flavor of feline coat coloration, “salmiak,” is associated with a 95-kb deletion downstream of the KIT gene.
Anderson, H., Salonen, M., Toivola, S., Blades, M., Lyons, L.A., Forman, O.P., Hytönen, M.K. and Lohi, H. (2024).
https://doi.org/10.1111/age.13438
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