Currently, the only tag types are Private tags (that only the individual can see) or Public tags (that everyone with access to the conversation can see).
It would be a cool feature to have "Private public tags," which would be public tags that only certain people can see on a conversation, despite who has access to the conversation.
For example, Users A/B/C have access to conversation Z. I apply a "Private public tag" to that conversation that both Users A/B can see on conversation Z, but User C cannot see that tag on the conversation, despite having access to the conversation overall.
I can see a lot of use cases for this as a way to track oversight of certain conversations without notifying/bothering specific people with a tag that everyone can see.