A search on the net lists ‘may well’ as B2 by Cambridge: ‘if you say something may well happen, you mean that it is likely to happen.
C1 point 184 in the category of MODALITY:
The usage associated with this grammar structure on the English Grammar Profile is:
to give emphasis to something unexpected
However, when looking at the examples, it seems like ‘conceding before giving reasons for one’s own opinion’. The other noticeable point is that most of what is connected to this form is either an adjective, passive or perfect form.
Here’s a look at the top 50 infinitives following “may well” on the NOW corpus:
1 MAY WELL BE 32229
Further collocations with “may well be”:
1 TRUE (JJ ) 542
2 ANSWER (NN1 ) 210
3 GREATEST (JJT ) 137
4 TEMPTED (VVN ) 118
5 REMEMBERED (VVN ) 111
6 CORRECT (JJ ) 106
7 WORRYING (JJ_VVG@ ) 68
2 MAY WELL HAVE 13382
1 BEEN (VBN ) 4210
2 GONE (VVN ) 124
3 SAVED (VVN ) 117
4 CONTRIBUTED (VVN ) 102
5 INFLUENCED (VVN ) 44
3 MAY WELL PROVE 912
4 MAY WELL FIND 885
5 MAY WELL BECOME 848
6 MAY WELL SEE 808
7 MAY WELL COME 716
8 MAY WELL END 675
9 MAY WELL TURN 671
10 MAY WELL GET 602
11 MAY WELL GO 490
12 MAY WELL TAKE 466
13 MAY WELL MAKE 450
14 MAY WELL DO 433
15 MAY WELL NEED 418
16 MAY WELL ASK 399
17 MAY WELL LEAD 395
18 MAY WELL FEEL 388
19 MAY WELL DECIDE 342
20 MAY WELL CHANGE 326
21 MAY WELL LOOK 268
22 MAY WELL WANT 239
23 MAY WELL MEAN 234
24 MAY WELL CONTINUE 230
25 MAY WELL FALL 226
26 MAY WELL HAPPEN 214
27 MAY WELL HELP 211
28 MAY WELL RESULT 201
29 MAY WELL BRING 190
30 MAY WELL DEPEND 187
31 MAY WELL GIVE 187
32 MAY WELL LOSE 181
33 MAY WELL PLAY 176
34 MAY WELL KNOW 173
35 MAY WELL THINK 161
36 MAY WELL FACE 155
37 MAY WELL START 152
38 MAY WELL PROVIDE 149
39 MAY WELL INCLUDE 147
40 MAY WELL PUT 142
41 MAY WELL DEFINE 132
42 MAY WELL WIN 130
43 MAY WELL REQUIRE 128
44 MAY WELL WONDER 128
45 MAY WELL REPRESENT 127
46 MAY WELL INCREASE 126
47 MAY WELL FOLLOW 125
48 MAY WELL HOLD 125
49 MAY WELL SAY 125
50 MAY WELL DETERMINE