A system is provided that includes a compressor section, a turbine section, a first engine and a second engine. The compressor section includes a compressor rotor. The turbine section includes a turbine rotor configured to drive rotation of the compressor rotor. The first engine includes a first engine inlet, a first engine outlet and a first engine combustion zone fluidly coupled with and between the first engine inlet and the first engine outlet. The first engine inlet is fluidly coupled with and downstream of the compressor section. The first engine outlet is fluidly coupled with and upstream of the turbine section. The second engine includes a second engine inlet, a second engine outlet and a second engine combustion zone fluidly coupled with and between the second engine inlet and the second engine outlet. The second engine inlet is fluidly coupled with and downstream of the compressor section.

A propulsion system for an aircraft includes an engine assembly, an interburner, a turbocompressor, and a flow control assembly. The engine assembly includes an engine. The engine includes an air inlet, an exhaust outlet, and an engine output shaft. The interburner includes an interburner inlet and an interburner outlet. The turbocompressor assembly includes at least one turbocompressor. The at least one turbocompressor includes a turbine and a compressor. The turbine includes a turbine inlet and a turbine outlet. The compressor includes a compressor inlet and a compressor outlet. The flow control assembly includes an engine exhaust diverter subassembly and at least one compressor outlet diverter subassembly. The engine exhaust diverter subassembly is connected to exhaust outlet, the interburner inlet, and the turbine inlet. The at least one compressor outlet diverter subassembly is connected to the compressor outlet, the air inlet, and the interburner inlet.