If the aircraft is owned by a company and flown by a company employee on a service for company only purpose where no revenue is earned on such flights then it can be considered private. However the stumbling blocks are when the aircraft starts to need multi crew, the issues come about when you may need a training and check process etc... Paying an independant pilot to fly your own plane starts to get into a grey area. The law does not stipulate the aircraft making revenue, rather whether the pilot receives reward/payment for the flight.
Simple pub test, I can hire an aircraft and fly it privately for my own purpose and the owner can profit on from it. But I can't hire myself to somebody and call it a private flight.