Let's take the 737NG as an example. The 737NG has a maximum certified altitude (MCA) of FL410.
Please note that I am getting this information from FSX with the PMDG 737. Though a simulator product, it claims to be very accurate model of the plane.
Also, although I am not sure, higher altitudes = fuel savings right?
So this rose the question: Can/May I fly above the maximum certified altitude?
Can I fly safely with an 737NG at 45,000ft for example?