Place one (or more) buttons on a block page for one or more specific groups of authenticated/identified users that allows them to override the block for ALL users for 30 mins/60 mins/24 hours/permanently.
Example use case: Teacher (authenticated/identified user) is able to override block on a specific Weapons category web site for an hour to allow the students (other users) doing fencing as an elective sport to examine/purchase equipment online.