If the party owns the aircraft and hires you, it shouldn't be a big deal. It's essentially corp flying under Part 91. If the party rents or leases the aircraft and contracts your services separately, you should be good too. However, the latter is pretty much known as Part 134.5 and if an accident or incident occurred, you better have a great lawyer! Tread lightly, you don't want to ruin a budding career by breaking the rules for a few hours in the logbook.