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Figuring out a theoretical key signature like that is the onerous part. After that find the various modal key signatures is comparatively easy.

What is the locrian key signature using 12 sharps? It's the seventh scale degree of B# major, which is Cx, and so Cx locrian has a key signature of 12 sharps.

Figuring out a theoretical key signature is the onerous part. But, after determining the theoretical key signature, finding the various theoretical modal key signatures is comparatively easy.

What is the locrian key signature using 12 sharps? 12 sharps minus 7 shaprs is 5 sharps, which is B major, so 12 sharps is B# major. The locrian mode starts on the seventh scale degree of B# major, which is Cx, and so Cx locrian has a key signature of 12 sharps.

Nevertheless, 7 sharps is C# major, 5 sharps is B major, basically adding 7 sharps to a key signature of up to 6 sharps will just add a sharp to the tonic, in other words 5 sharps in B major, add 7 more sharps, it becomes B# major. You sort of 'reset' adding sharps at the F, but make them double-sharps and add 5 of them, so Fx Cx Gx Dx Ax then the rest will be plain sharps until you have 7 total changes to the gamut of letters by fifths FCGDAEB, so E# B#, altogether the key signature of "12 sharps" for B# major is Fx Cx Gx Dx Ax E# B#.

Nevertheless, 7 sharps is C# major, 5 sharps is B major, basically adding 7 sharps to a key signature will just add a sharp to the tonic, in other words 5 sharps in B major, add 7 more sharps, it becomes B# major, or add 7 sharps to C# major makes it Cx major. 

You sort of 'reset' adding sharps at the F, but make them double-sharps and add 5 of them, so Fx Cx Gx Dx Ax then the rest will be plain sharps until you have 7 total changes to the gamut of letters by fifths FCGDAEB, so E# B#, altogether the key signature of "12 sharps" for B# major is Fx Cx Gx Dx Ax E# B#.

I don't know why you want a system to handle 12 sharps. After seven sharps or flats, key signatures become theoretical key signatures. Those are normally used, and they wouldn't use up to 12 sharps/flats anyway, they would use double-sharps/double-flats.

Nevertheless, 7 sharps is C# major, 5 sharps is B major, basically adding 7 sharps to a key signature of up to 6 sharps will just add a sharp to the tonic, in other words 5 sharps in B major, add 7 more sharps, it becomes B# major. You sort of 'reset' adding sharps at the F, but make them double-sharps and add 5 of them, so Fx Cx Gx Dx Ax then the rest will be plain sharps until you have 7 total changes to the gamut ABCDEFG, so E# B#, altogether the key signature of "12 sharps" for B# major is Fx Cx Gx Dx Ax E# B#.

I don't know why you want a system to handle 12 sharps/flats for key signatures. After seven sharps/flats, key signatures become theoretical key signatures. Those are not normally used, and they wouldn't use up to 12 sharps/flats anyway, they would use double-sharps/double-flats, with only 7 total signs in the key signatures.

Nevertheless, 7 sharps is C# major, 5 sharps is B major, basically adding 7 sharps to a key signature of up to 6 sharps will just add a sharp to the tonic, in other words 5 sharps in B major, add 7 more sharps, it becomes B# major. You sort of 'reset' adding sharps at the F, but make them double-sharps and add 5 of them, so Fx Cx Gx Dx Ax then the rest will be plain sharps until you have 7 total changes to the gamut of letters by fifths FCGDAEB, so E# B#, altogether the key signature of "12 sharps" for B# major is Fx Cx Gx Dx Ax E# B#.