Is anonymous posting possible?

I was actual positively surprised when I read that

I think that if the transparency you’re asking for ever becomes available as a site setting, it should be clear to users that their anonymous ID is only anonymous for non-staff.

Going in the other direction, I wonder if discourse is already maxed out in terms of how far it can technically go towards real anonymous posts, i.e. where not even admins can find out who posted something. I know that corporate clients require this from group support systems like meetingsphere in order to guarantee employees (or whoever participates in a session) absolute anonymity. Meetingsphere achieves this by deleting a temporary ID as well as IP addresses after the user has logged out. The result is that it is not only impossible to tell who posted what but also which two contributions come from the same individual.

While this is obviously a special use case, especially in brainstorming exercises, it could be interesting for discourse to support it, but I’m not sure if it’s even possible, given how discourse is built.