Hi Alan,
Many thanks for the added explanation, based on what you describe, this would indeed be a case which would require the object-based capabilities which are yet unsupported by Groups.
What might work for you could be a customized implementation that relies on the membership info from Groups and hooks into WordPress filters to determine whether a user has or has not a certain capability. This could be based on the group membership of the post creator and the user for which a capability would need to be evaluated.
So when a WordPress capability to edit a post is evaluated, you could hook into the user_has_cap filter, look at the post to get its author, get the groups to which the author belongs, then check the groups for the current user and evaluate the result for the filter accordingly.
Thinking about it that way, I think it should be quite easy to implement for a particular case. It’s more difficult when trying to generalize it, but that shouldn’t be a concern in this case.
I hope that makes sense, do let me know if you have questions on the suggested solution.