This sounds like an X-Y problem. You're not explicitly stating it, but it's implied this interface is to assign permissions to groups of people, rather than assigning permissions to each individual.
Because individual assignings would result in lots of double work. Assigning them to a selection reduces that by a lot. But you would still have to manually select users every time you use the interface, which is also creating double work.
So, create groups, and put people in them. Then assign permissions to them. Yvonne mentions roles, which are a specific kind of group. It'd be pretty easy to hardcode, and if that solves your problem, great!
But sometimes you need to be more flexible in selecting groups of people. For example by store location & role & product range. For example Chicago, Sales, Electronics. Then you need to come up with your own kind of taxonomy. This could be a simple top-down structure like:
But it can also be a more tag-like system, where you have to be in all 3 groups to have access to Chicago electronics' sales figures. Sort of like a venn diagram.
You can of course combine various methods, for example a simple role schematic (employee/manager/director/admin) combined with tags to allow people to view just their own data, to edit their own data, to access all databases from a given location, or give all-access.
I'm not going into details because A; I don't have enough info, and B; going from individual selection to groups is a pretty broad change of direction instead of tweaking a specific system.