Definately not impossible!!
I work for a company that provides this service. My earlier post must have been blocked because I inluded a phone number and link to our site.
Our software accessable via a web portal, uses suppliers CSV call data to produce itemised billing. Users can log on and tag their calls as personal or business. The calls can default to personal or business depending on customer preference, time of day or any other criteria.
The system also includes a method to allow mangers to approve personal calls and a method for administrators to manage the payment for these personal calls.
This process has saved some of our customers tens of thousands of pounds a year.
It is possible and it is worthwhile.