WordPress multisite: one site at / and another at /folder

Hello,

I currently have wordpress installed in mydomain.com/ with pretty links enabled. Meaning users can do the following: mydomain.com/members/ to reach the members page.

I was wondering if its possible to setup ANOTHER wordpress site at mydomain.com/internal/ that would only be allowed for certain users. I saw on the documentation that it can either be done by subdomains (which I cannot do) or through sub-directories. I want to do sub-directories but not make my users go to mydomain.com/site1 and mydomain.com/site2. Instead, I’d rather everyone else keep going to mydomain.com/ and have a smaller set go to mydomain.com/internal

Thanks!