may have + PAST PARTICIPLE

In the English Grammar Profile, B2 point 163 MODALITY is defined as:

‘may’ in phrases such as ‘as you may know’, or ‘as you may have’ + ‘-ed’ to focus the reader on shared knowledge.

This partly overlaps point 168 MODALITY and  PAST AFFIRMATIVE of

‘may have’ + ‘-ed’ to talk about possibility in the past.

A search for collocates of ‘may have’ in COCA:

Past possibility example:

He said he believes drug use or mental illness may have contributed to Carter‘s behavior, but that hasn’t been confirmed.

A search on iWeb for as you may * * * *:

1 AS YOU MAY OR MAY NOT KNOW 950

As you may or may not know, big things are happening here in Williamsburg, Brooklyn.

2 AS YOU MAY HAVE NOTICED , THE 288

As you may have noticed, the chat function has disappeared from the top of the Forum.

3 AS YOU MAY HAVE GUESSED , THE 227

  Happy

Drawing eyes on the butts of cows is highly effective in scaring away lion predators, study finds

As you may have guessed, the major success was with the extra pair of eyes on the behind. It worked so well that over the four-years, none of …

4 AS YOU MAY HAVE NOTICED , I 201
5 AS YOU MAY HAVE NOTICED , WE 194
6 AS YOU MAY BE ABLE TO TELL 189
7 AS YOU MAY NOT BE ABLE TO 189
8 AS YOU MAY HAVE GUESSED FROM THE 184
9 AS YOU MAY ALREADY KNOW , THE 181
10 AS YOU MAY HAVE ALREADY GUESSED , 171
11 AS YOU MAY BE AWARE , THE 159
12 AS YOU MAY KNOW BY NOW , 143
13 AS YOU MAY HAVE HEARD , THE 136
14 AS YOU MAY OR MAY NOT BE 130
15 AS YOU MAY HAVE GUESSED , I 127
16 AS YOU MAY HAVE GUESSED , THIS 125
17 AS YOU MAY OR MAY NOT HAVE 113
18 AS YOU MAY HAVE GUESSED BY NOW 112
19 AS YOU MAY HAVE ALREADY NOTICED , 106
20 AS YOU MAY ALREADY BE AWARE , 102