Burp Suite Enterprise Edition supports simultaneous access by multiple users, and lets you configure role-based access control (RBAC).
You can define roles within the application, or use the predefined roles:
You can define groups that are tied to sets of roles, or use the predefined groups:
You can define as many users as you wish (there are no licensing restrictions on numbers of users) and place users into groups to determine their access:
In addition to the vertical segregation of privileges offered by roles and groups, you can also enforce horizontal segregation of privileges by creating groups that are restricted to certain sites: