Do airline SOPS generally permit flying close to or at the operational ceilings of commercial jets?
Forget the hype on FL 400 and above.
Think about ceiling (theoretical), Max fligh altitude (don't go there) and optimumflight level.
Cieiling is, very broadly defined as the max altitude an airplane is capable of, and still complies with regulation requirements in terms of handling and most of all performance after depressurization.(That's an awfully broad a statement, believe me !)
Max flight altitude is,
for a given weight, the fabled "coffin corner", with a margin for wing loading, generally 1.3 g, which means that your airplane won't stall during a ~40° bank, or encounter some heavy turbulence. At that altitude, the aircraft has been certified to fly safely without any problems ( engines are certicated, too).
Please remember that the altitude performance of an aircraft improves with lightening weights. For instance the initial FL of a loaded 744 is about 300 at the beginning of the flight and 390 eleven hours later. In seven years with the 744, I've never been able to climb higher than FL 410.
There is nothing in the FCOM or the SOPs to prevent you from flying at that altitude during the course of a trip, although you'd be away from the most economical cruising altitude, which would be :
The Optimum flight level.
Try and find the Airbus text on High altitude flying (The "getting to grips with Aircraft performance" and ..."fuel economy"...and "...cost index" will do you fine.)Let me know if you can't find them.
Regards