Porterjet’s answer is pretty spot-on. Many business jets have service ceilings thousands of feet higher than manycommon airliners.
Airliners:
A318, 319, 320, 321 - 39,000ft
B737 - 35000 to 41000, depending on series.
B757 - 42000ft
Business:
Gulfstream II, III, IV, V - 45,000 to 51,000ft
C750 - 51,000ft
Falcon 2000 - 51,000ft
Lear 45 and 60 - 51,000ft
Global 5000 - 51,000ft
Many times the commerical jets are able to climb higher only well into the flight, after they burn off fuel. (actually this can happen to any jet but it seems that it happens to airliners more often.)
Say you’re joining an enroute airway that is packed, leaving very little or no in trail spacing. Outside of fuel burn, you might find more empty slots on that airway at the higher altitude, so not only do you save on the fuel, but you don’t have to deal with all of the traffic below you until you reach TOD.
Concorde had a maximum cruise altitude of FL600 -60,000 ft. Typical cruise altitude was FL550 or FL560. Let me tell you, It’s really annoying to be sitting at FL510 and watch the Concorde streak overhead…cool, but annoying.
Anyone with a “little” extra cash can go to Russia and take an edge of space flight in a MiG-25. That’ll get you to 90k’ altitude. Always been another dream of mine…