To make it quick and simple, the service ceiling is the maximum altitude at which an aircraft can still maintain a rate of climb of 100 ft/min.
You have also the absolute ceiling, which is the altitude where the climb rate becomes 0 ft/min.
And finally, you have the operational ceiling altitude limit imposed by certification, systems, or operations (pressurization, oxygen, regulations, etc.).
So, you can indeed have an aircraft that is capable of climbing much higher but is limited by its system(s), most of the time the pressurization (how the system is built, how the airframe can handle a bigger differential, how fast can you descent in regards of oxygen (for pax mostly as the oxy for crew is generally more than enough while for the pax it's very limited in time)).
So, it's not only what the aircraft can do by itself, it's more of a global picture : powerplant, airframe, system(s), oxygen (passengers limitation mostly), etc...
Not talking about the YS-11 in particular, but in general.