I will admit - I am a bit confused. I believe my comprehension is restricted due to terminology. let me try and simplify what I am saying and see if that helps. We are going to figure this out one way or another - lol.
Looking at the normal module structure, there are a few things you can do within each module. So, lets identify a few of those first. We have Add/Create, View, Browse, Search - to name a few.
And, just for the sake of putting it out there - we have several modules - such as Groups, Events, Photos, Sounds, Files - to name a few.
Then - we have membership levels. The default ones are non-member (anyone not logged in), Standard, and Promotional. You can create custom membership levels - and charge a cost for them as well.
For my example, we will use the standard, and 2 custom membership levels - Level A and Level B. And create 3 new members - User A, User B, and User C.
now - by default, here is what is possible:
You can assign user A as membership Standard
You can assign user B as membership Level A
You can assign user C as membership Level B
From here say,:
You only want User A (Standard membership) to be able to view Groups, but not able to add a new Group
You only want User B (Level A membership) to be able to view Groups, and search Groups and able to add a new Group, but not able to view Events
You only want User C (Level B membership) to be able to view Groups, and view Events, but can not search Groups, as well as able to add a new Group and add a new Event
These are just some of the quirky scenarios that are possible. Which leads to the drawback - the potential for having a lot of membership levels is there - depending on how you want to group your members.
If you are looking for a "by member" type setup similar to above - I do not know of any personally. Maybe someone will decide to create one.
Last possibility - you have a module that allows you to add a new event within a particular "group". If this is the case - the original explanations already provided would be the exact same answers.