Private airliners operate in exactly the same way as their commercial cousins.Provided the runway is long enough and the pavement strong enough to support the aircraft their ops teams would simply request handling from whoever they wanted to attend the aircraft. In the case of a jet that can't self support stairs or ground power etc then the agents might have to source them temporarily (at a cost) but otherwise so long as the airport supports the type, there is no restriction where you can take it.