Piston engines got pretty wild before turbines eventually took over the world.  The most efficient ones were more efficient than today's turbines in terms of BSFC[0].  One of the most interesting to me was the Napier Nomad[1], which used turbo- and super-charging.  However, the turbo had secondary fuel injection and effectively ran as a turbine to drive the compressor.
[0]https://en.wikipedia.org/wiki/Brake-specific_fuel_consumptio...
[1]https://en.wikipedia.org/wiki/Napier_Nomad