Depending on which corporate entity is the OWNER of the corporate jet, then the
flights might NOT be for persones employed by that entity.
All you need then is a lease agreement to keep it Private. Different scenarios for when the A/C owner is offshore and the end user is onshore, you can even nominate a UK co as agent for the offshore entity to claim back VAT on purchase and fuel etc.
There is no legal reason to have a private A/C on an AOC and those that do are just misinformed or misguided. The only advantage is fuel tax, but there are ways around that too for private aircraft.