Maximum ceiling
Another factor limiting max ceiling is the requirement to return to (I believe) 15,000ft within 4 minutes - so wing design, speed brakes, MMO/VMO are all factors that contribute towards how fast an aircraft can descend and therefore the maximum attainable rate of descent can be a limiting factor in setting the service ceiling. Thrust is not always a factor - I believe the GLEX, G550 and C-750 engines are all designed to operate up to FL600.
As previous posts have noted, even though these aircraft all have FL510 as a ceiling, completions and empty weight are usually too high for the majority of these aircraft to reach or maintain FL510 for any useful length of time.
We operate a Global Express and similar to the G-IVSP that I used to fly, we target FL390-FL410 as our initial cruise altitude, step climbing several hours later to FL450. ISA and weight are the two controlling factors. The Global wing is optimized at M0.83, with normal cruise at M0.85 - long range cruise is usually a function of optimum TAS, but can be as slow as M0.77 for a 12 + hour leg.