Full Idea
It seems that we cannot say "Nixon might have been a different man from the man he in fact was", unless we mean it metaphorically. He might have been a different sort of person.
Gist of Idea
We cannot say that Nixon might have been a different man from the one he actually was
Source
Saul A. Kripke (Identity and Necessity [1971], p.176)
Book Reference
'Meaning and Reference', ed/tr. Moore,A.W. [OUP 1993], p.176
A Reaction
The problem is that being a 'different sort of person' could become more and more drastic, till Nixon is unrecognisable. I don't see how I can stipulate that a small and dim mouse is Richard Nixon, even in a possible world with magicians.