Not sure how best to describe this so here we go -
Say domain www.domain.com is blocked, rather than just denying the request outright, take the user to a general 'Blocked by pi-hole' page (hosted on the pi-hole instance), informing what happened and optionally with the pi-hole admin's e-mail address to report an issue / request unblock (or alternately a more advanced notification that would come through the admin console). This feature would be optional, turned on or off by admin. Taking it a step further, ability for admin to enable option on this block page for user to choose to proceed anyway to the blocked page, would not alter block / white lists but essentially function as a temporary exception for that client lasting x minutes (x being a default pre-defined by the admin in console).
Additionally, unsure how easily this could be implemented, stand in images of the pi-hole logo that replace blocked images. Again the ability to toggle this on/off by admin. Images could be linked to take user to a page like the first part of this request, essentially informing what happened and again with optional ability to notify the admin of issue and optional ability to grant self a temporary timed exception (for that client only).