I'm not sure if "a user with more power than root" would be the right way to describe that. The code would have a permission that "root" doesn't, but I wouldn't call the code "a user". It's a Unix idea that "a specific set of permissions" and "a user" are synonyms. Systems can exist where some permissions aren't represented as users.
The kernel has a number of things it can do: if you try to do a special thing it could force authentication itself - eg a “root”/admin user can still do the action, but a process with “root privileges” cannot, it can require the process attempting the action have correct entitlements, it can simply reject the operation entirely, etc. it can do all of the above: I recall there being some operations that can only be performed by specific apps, with specific entitlements, as special users, with immediate authentication (startup items and the like)
chris@chriscomp /usr/bin # sudo su root
root@chriscomp /usr/bin # touch testo
touch: testo: Operation not permitted