It is extremely rare to have 5 verbs in a row in English. For this reason, we think this modal verb + perfect progressive passive structure is a C2 marker.
A search in the NOW corpus for:
_VM _VH been being _VVN
1 MIGHT HAVE BEEN BEING RELEASED 3
2 MAY HAVE BEEN BEING HELD 2
3 SHOULD’VE BEEN BEING REPLACED 2
4 SHOULD’VE BEEN BEING EXECUTED 1
5 MUST HAVE BEEN BEING BULLIED 1
6 MUST HAVE BEEN BEING BROUGHT 1
7 MUST HAVE BEEN BEING BETRAYED 1
8 MIGHT HAVE BEEN BEING TOLD 1
9 MIGHT HAVE BEEN BEING SMUGGLED 1
10 WOULD HAVE BEEN BEING WHISPERED 1
11 WOULD HAVE BEEN BEING USED 1
12 WOULD HAVE BEEN BEING TIED 1
13 WOULD HAVE BEEN BEING CELEBRATED 1
14 WOULD HAVE BEEN BEING ATTACKED 1
15 WILL HAVE BEEN BEING DEVELOPED 1