Hi Sean
This is indeed a tough one.
Let's give the "field" we are talking about a name, i.e. "role".
A member joins a group and has a designated role in that group, but the available roles change from group to group.
The field has to be a relationship field because it is particular to the connection between member and group (e.g. John Smith could be President of the Juggling Club and could also be Secretary of the Archery Club while Jane Black could be Secretary of the Juggling Club etc. etc.).
So the challenge is that when connecting a member to a particular group, e.g. the Archery Club, only the roles relevant to that group are available.
This, for sure, would involve some code, it's not something that can be done within the UI.
There would be two parts to this.
The first is that you need to record somewhere what the roles available to the different groups are. In principle that would involve creating a field "Group roles" that includes all of the available roles. (The specifics of what field type would depend on the full implementation.)
That's kind of the easy part.
The next is that you would have a relationship field for the actual role, and somehow that field would need to be dynamic, such that depending on which group the member was being added to, the available options in the role field would be modified.
If the starting point was the group, and you were adding a member to it, then it's feasible that we know the group and so can modify the options available in the role field.
If the starting point was the member, and we were connecting to an existing group, that becomes trickier. I'm thinking here about the UI, and whether we are operating in the back end with PHP or the front end with JavaScript.
Before commenting more, I would need to know more about where this data is being added, what's the context? Back-end editing screens? Front-end forms? What's the starting point in the workflow?
Note, as indicated, this is going to require coding, and I can't do that for you, but I may be able to point you in the right direction if I have some more details.