Allow organisations to included attested membership / credentials in ID assertions or certs

One use case is allowing an industry group / organisation to define a list of members / participants / organisations that meet some criteria, like the UK's GMC (https://www.gmc-uk.org/), or the IPTC's Verified News Publisher programme.

This might be via Verifiable Credentials, or some other mechanism. In terms of embedding, finding a low-payload-size mechanism would be preferable, so it would be good if we could investigate with Certificate Authorities if carrying this data in a certificate would be possible.

I wonder if others in the Verifiable Credentials community have considered something similar before?