That is, suppose that I am at item n and I want to make a reference to item n - 3 without explicitly specifying it.
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Is it possible to get the current item number and perform arithmetic on it in enumerate environment?
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How about
Here's a complete MWE:
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\labelitem n-3 and\refit. Probably you should clarify better your question. – egreg Mar 4 at 22:01