So to understand your current set up: you currently create 2 teams per client one internal and one external? While this could work, it may create a lot of housekeeping issues as you grow your client base.
Yesterday I posted a tip on how to use such scenario if you have access to the Portfolio feature. Here is the article:
It is worth directing you to 2 different articles that could give you some insights:
If you do not have access to Portfolio feature, then some tips from my article might assist you.
I would suggest using the multi home feature as well where necessary between your internal and external projects. So you create a single team per client. External Project is where the client gets access to their engagement and the internal project you keep locked and only visible to your internal team for any approvals or reviews.