Have a look at the Group module which is like a "little brother" of Organic groups. It only started in D7 and with a D8 version in the pipeline. Personally I'm more and more considering/using it as a potential alternative for the Content Access module. And since it is all entity based, there are lots of ways it can be used in combination with the Rules module also.
Specific to your question here, I think what is going to help you a lot is the Group member profiles sub-module.
For way more details about this module, refer to its Community documentation pages, such as the Group HowTos subpage of it.
Note: Your question doesn't specify which version you are using, but this answer applies for both D7 and D8.