A bit of a loaded question, like how are you defining the aircraft; without all the systems and weapons is it still the same aircraft? Do you require the ability to use certain abilities, like supersonic travel or is it more of a collectors item?
Anything can be bought if the stack of cash is tall enough, even permission to own a particular jet. Though this permission may have details like it must stay in the national airspace, file special flight plans so the location is always known, and maintenance can only be performed by certain companies.
You could even get an F22 built with custom non-classified flight systems, of course this custom development would cost a bit extra, really it would essentially be ordering a one-off experimental that looks like an F22, and we are back to how you define the aircraft. Plenty of other types that are less classified are still in production, such as the F18 and F16 would likely be available to a civilian with more reasonable modifications.
Assuming this is for flight over land the speed is limited to less than mach one, and if you don't need the low radar profile, there are better designs for sub-sonic high performance flying. Fighters have many considerations other than pure flight: armor adds weight, aerodynamic effect of externally mounted weapons(and the frame mounting hard-points), weight of the internal weapons, those guns change the balance and useful load, targeting systems, active radar and counter-radar systems, passive radar reflection, heat signature, cameras, flight with damage. All of this detracts from flying performance.