British National Corpus (BYU-BNC) has 122 examples.
'Of' may follow 'may', as we saw in your second 'May (of necessity)' example, but there is no expression 'may of'.
The modal perfect 'may have (+ past participle)' is often pronounced as /meɪəv/. As this sounds the same as 'may of' would, if it existed, some people incorrectly write it as 'may of'.
Well, I looked through the first 50. They include examples of a word missing, a couple of typos for 'many', several examples of the 'May of 1984' type, a couple of the 'may, of necessity' type, and several examples of the mistake I mentioned in my last post.
I repeat, there is no expression 'may of'.
Here is one example, fom BNC: reference to er information or er material that may of significance. It will be interesting to know how the wha how the minister
Sadly, the misspelling of "may have" as "may of" is rife, even amongst some of my otherwise well-educated and well-read friends. I see an alarming number of examples of:
ALL of which are incorrect, by the way, if anyone was in any doubt, when the "of" should be "have".
Apart from the two examples already cited ("may of necessity" and "May of 1984"), there is no expression "may of".