No, thanks, that's not necessary.
Generally speaking, an 11+ test in one authority might not be acceptable in another authority, because there is the issue of whether the standard of the two tests is comparable.
If we were talking here about two VR tests in the same area, with the same format, the same standardisation, the same sort of cohort, I can see they might be viewed as more or less comparable.
Throw in a curriculum subject such as English, and it could become more complicated. Might we be talking about an essay or a comprehension, marked by different people?
To get to the point, however, I've never heard of an appeal based simply on another 11+ result. Usually this would be just one part of the alternative academic evidence presented to an appeal panel. It would be up to the appeal panel to decide whether the alternative 11+ result was comparable, and, if so, how much weight to give it.
With regard to grounds for appeal, the Code of Practice says:
Where there is no local review process ..... or no local review process has been applied, the panel should consider any factors which appellants contend may have affected the childâ€™s performance (e.g. illness, bereavement); whether the family made the admission authority aware of these before they sat the test; and whether it offered alternative testing arrangements or made reasonable adjustments (e.g. in the case of children with disabilities). The panel may then need to consider any clear evidence presented by the appellants to support their claim that the child is of the required academic standard e.g. school reports giving Year 5/Year 6 SAT results or a letter of support from their current or previous school clearly indicating why the child is considered to be of grammar school ability.