Richard Lugg carried out a turbojet project with axial compressor and multiple turbine. It is officially patented.

“R. Lugg's turbojet” (from the patent)

Author's note: The turbine has many stages and by the simplest principles of physics, they should not be of decreasing diameter, but rather increase their diameter or frontal area, since the gases lose energy at each stator-turbine stage. That is why if we look at the current large turbofan, the shape of the cowling that contains the turbines is like a growing bulb so that each step has a greater area. Less energy in the gases is compensated by more area in the turbine and in each subsequent step.

"Observe the group of turbines"