What are the characteristics of business jets that allow them to cruise at higher altitudes?
Many things, probably the most important of which is money.
For any aircraft to get up very high, you need a low wing loading (i.e. weight vs area), and a fair bit of power. You’d also need to be able to cruise at high mach number. That implies a thin, highly swept wing, which in turn tends to be more demanding at lower speeds.…i.e. higher stall and min drag speeds. Assuming a min drag speed of 230 kias, that converts to a mach number of almost .94 at FL500. So you can’t go slower than that, and faster will definitely have you into the transonic nasties (limited control, pitch changes, drag rise).
The U-2 takes a different tack, with what is a very slow speed wing, but its stall and min drag numbers are so slow that mach number isn’t an issue until much higher.
Structurally it will have to be strong enough to handle the increased differential pressure that will be needed, and your pressurisation system will have to be up to it. Much easier in a biz jet than an airliner.
It’s not necessarily all that efficient, but the airways generally stop at F450, and airliners very rarely go above FL410, so the ability to go high could make it easier to get ATC clearances. The average pilot has no business up there though.
Airbus are limited to FL431 and modern Boeings to FL451. 99.9% of the time they couldn’t get there even if you wanted to.