Pets travel in-cabin on a private jet — no cargo hold, no crate restrictions, no temperature-or-pressure exposure. For brachycephalic breeds (French Bulldog, Pug, Persian cat), this is the only safe option for long-haul travel.
Documentation: an EU pet passport for intra-Schengen travel, a USDA APHIS health certificate for US arrivals, and country-specific entry permits for the UK (TRACES NT), UAE (MOCCAE permit) and Switzerland. Lead time for documentation is 10 to 21 days depending on destination.
Some operators levy a cleaning surcharge for animals; most do not. Catering can include curated pet meals on request.
Operationally, no aircraft type restriction applies — pets fly equally on a Phenom 300 or a Global 6000. The constraint is purely the regulatory entry documentation at the arrival country.