Test pilots have reported that a Gulfstream G550 airframe can handle supersonic flight, and the BR710 turbofan engines can handle it. The limit is the engine intake design.
With an optimized intake, its entirely possible the fuel consumption at M2.2 would be comparable to ~M0.98
that is one of the major issues here. Modern turbofans on large passenger planes like 787, 380, etc... are that efficient in major part because of high by-pass ratio. Which is not really an option for 2Mach+ speed.
As somebody mentioned, more comfortable 0.85Mach flight would be preferable in many situations to uncomfortable and very expensive 2Mach. If i were starting something like this i'd go straight for suborbital SFO to Singapore in under couple hours. Technology-level wise not that different, money is no issue in that segment (Branson's $200K is not that far from super-premium-business class for your priceless CEO) and there is always large money-no-issue fallback customer - military.
There has never been a supersonic passenger aircraft built with modern turbofan engines.