I would like to know for example if someone can take the "core" of an CFM56 used on A320, redesign it by adding a supersonic intake, a convergent-divergent nozzle, and reduce its bypass ratio, but keeping the same stages of compression and turbine stages. Will it be able to achieve supersonic speeds?
This is more or less exactly what had been planned for the (now defunct) Aerion supersonic business jet. The engine was to be developed by GE, with the core of a CFM56, the fan replaced with a lower bypass fan, inlet and exhaust replaced, and that's it. The core was to be off the shelf CFM56 core.
Also, the F101 and F110 fighter jet engines and the CFM56 share a very similar core. It's not exactly the same, but it's fairly close.