There's nothing, anywhere in the rules, anywhere, that restricts who can fly what, other than the requirement to be endorsed on the aircraft.
The flight manual of the aircraft may specify minimum numbers of crew - and this may be different depending on whether the aircraft is operated VFR or IFR.
The Sultan of Brunei's A380 is a good example. Its operated privately, so you can fly it with a PPL and appropriate ratings. Whether he actually HIRES private pilots or not is up to him.