Would driving one of these engines concurrently with the power generated by a turbine engine make sense? Does the thrust generated by a turbine engine hit some

Would driving one of these engines concurrently with the power generated by a turbine engine make sense? Does the thrust generated by a turbine engine hit some point of diminishing returns that converting the engine energy to electricity and powering this engine be more efficient? I know Boeing have made advancements in the efficiency of drawing electric power from a turbine engine with the 787, the generators are now directly connected to the transmission of the engine.