Could an airliner get better fuel efficiency at higher altitude?
There are several factors to take into account to explain your question, but it is a nice one.

In a cruise flight the aircraft force balance determines that the lift compensates the weight of the air plane and the engine thrust compensates the drag. 

So, assuming the weight is given (which varies along the flight) the lift is determined to ensure the air plane is not falling. The lift influences the drag, the more the lift the more drag (actually a lineal variation with the variation of the square of the lift). And so, the engine compensates the drag.

So... engine thrust depends on the weight, essentially to the aerodynamic efficiency. So, my first answer, the more efficient the aerodynamic of the air plane, the higher it can fly. So, the engine is not the only factor.

However, you are highlighting an important point, the performance of gas turbine based propulsion. The problem of this propulsion is the need for an external oxidant. Essentially, the engine needs the oxygen of the atmosphere to be able to work. So that limitation requiring oxygen will make it impossible to reach much higher flight levels.

Another option is to change the propulsion concept and use an independent engine where not only fuel is carried but also oxidant is carried in the plane. The normal answer to that one is using a rocket engine. For example, the Bell-X (first manned A/C to flight faster than speed of sound) was having a ceiling of +90000 feet using rocket propulsion.