Elevate privileges for REST API

Is there a way to elevate privileges on a REST API call?

This is just theoretical. Lets say we wanted to create a wrapper for the Security Console. We want to allow users to perform some function on user accounts without actually letting them access the Security Console itself. Would that be possible?

Same thing could be said for some kind of HR-related function. Maybe an Assistant can perform a specific REST API call but not be given overall permission to that particular page, etc.