Well you used the example of Kane who was capped by NI, then capped by Ireland, before returning back to NI.
So I assumed you mean't the player had (or at least could have) played for Association B.
But you are obviously more clear about what you wrote than I was
The sands shift.
First I thought that a player only had to be capped at competitive underage level in order for the change to take effect. Then I thought it had to be a senior A friendly. Now I think it has to be a senior competitive cap, even if the FIFA man didn't spell it out.
But after his reply, it is becoming more clear that a player can move hither and thither, even between 3 associations, which explains how that player that Danny offered as an example, is on his 3rd association.
The one thing that is clear, that maybe everybody (except NB possibly) can agree upon, is that the literal interpretation of 'can only make one request to change' does not remotely cut the mustard. So we have to look for examples to prove the rule.
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