Settle for a Boeing BBJ (737-700 or 800 a BBJ1 or BBJ2) Far more readily available to charter than a 767 in exec config.
A319ACJ is a similar type of plane. Can anyone comment on the range (Japan-Europe, westbound) and comfort of 30...50 persons on a BBJ?
Charter VIP planes include a number of refurbished Boeing 757-200-s (better range and slightly bigger than BBJ).
There are a few older widebodies available for private charter - at least one 747-200. But most VIP widebodies, whether bought for VIPs or secondhand, are kept by governments and not offered for charter.
Lightning brought down a 707 in 1963, by fuel tank explosion. Airplanes have since got better lightning protection.
For a 737, or 757 or 767 or any other twin, one engine out requires landing on nearest suitable airport. They are not allowed to fly past airports even if they have fuel for longer one-engine flight. At least scheduled airlines under part 121 are not. What about charter, part 135? And what wiggleroom do crews have to call nearby airports unsuitable?
What about midair, like Legacy and 737 collision in Brazil? Legacy landed, for some reason 737 did not.