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A P337 is not certified about 20,000, so it is not "legal" to fly it up there.
Depending on outside air temperature and power setting, the P337 will frequently not maintain full cabin pressurization very much above 20,000. The rear turbocharger on this aircraft is the controlling factor.
According to the best information I have, the P337 will fly above 20,000 if you running a high power setting, and does fine up there. Above 25,000 is probably not practical.
To answer the next question that frequently comes up, no, there is no way to "turn off" the pressurization and use the turbo output just for the engines.
The T337 turbochargers are not the same units as the P337 (and it's not the same airframe, a different airplane really). The T337 turbochargers serve only the engines, and in that airplane, you can get a higher service ceiling assuming you have the right oxygen equipment (pressure demand mask above 25,000' if I recall correctly). Remember that 31,000 on the turbo is a true service ceiling - rate of climb less that either 50 or 100 fpm, I can't remember, and you are probably getting 55% power or something like that. The actual operating ceiling that one might really use is lower, perhaps in the mid to high twenties.
Kevin
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