Since there is inevitably a big change in the aerodynamic behaviour of any plane at Mach 1.0, there is a relatively limited speed gain to be had from pushing beyond Mach 0.85 before some parts of the airflow become transonic and the whole design would need to be changed.
The same applies to the air flow within the engine itself. Supersonic aircraft don't have large diameter, high bypass ratio, wing-mounted engines with (at least conceptually) simple intake designs.
From the customer's (i.e. the airline's) point of view, the simplest way to operate a plane is to be able to cruise at the same speed as everyone else when flying busy routes (e.g. transatlantic from Europe - USA), not by trying to jump the queue and save a few minutes.
It would certainly be technically possible to do what the OP proposes, but it's not economically sensible if either the customer or the manufacturer wants to run a profitable business.