The fuel efficiency of turbofan engines has improved significantly, hence reducing aviation's CO2 emissions. However, the increased operating pressure and temperature for fuel efficiency cause adverse effects on NOx emissions. Therefore, a novel engine concept, which can reduce NOx emissions without affecting the cycle efficiency, is of high interest to the aviation community. This paper investigates the potential of an intercooler and inter-turbine burner (ITB) for the future low NOx aircraft propulsion system. The study evaluates performance and NOx emissions of four engine architectures: a very high bypass ratio (VHBR) turbofan engine (baseline), a VHBR engine with intercooler, a VHBR engine with ITB, and a VHBR engine with both intercooler and ITB. The cycles are optimized for minimum cruise Thrust Specific Fuel Consumption (TSFC), considering the same design space, thrust requirements, and operational constraints. The ITB is only used during take-off to minimize cruise fuel consumption. The analysis shows that using an ITB solely, with the energy split of 75% (the first burner) / 25% (ITB), reduces the cruise NOx emission by 26%, and the cruise TSFC slightly by 0.5%. The intercooler alone reduces the NOx emissions by 16% and the cruise TSFC by 0.8%. The combination of intercooler and ITB reduces the NOx emissions further by 38%. The analysis confirms that introducing an intercooler and ITB can potentially resolve the contradicting effects of fuel efficiency and NOx emissions for the future advanced turbofan engine.