My firm has a strict staff travel policy which, in short, is economy for short-haul and WTP for long-haul. That said, it is possible to pay the difference personally between the allowed class of travel and business class. All of my travel needs to be booked through one of two portals but that allows two different GL codes to be specified. So I will bill the firm-chargeable amount to one GL code and the difference to my personal charge code. I then reimburse my employer either via cheque or direct payroll deduction.

Where things get a little peculiar is when it's possible to book a cheaper itinerary in business class than in WTP. That is 100% against policy. You would need to book WTP even though business class is cheaper. If business is literally a penny more expensive you can pay that yourself, but if it's a penny cheaper to fly in business then that's not allowed. However, at least the policy is now consistent across regions. Previously US-based staff flying to the UK or Europe could fly business class, whereas UK-based staff flying to the US could only fly in WTP.