Many turbulent combustion modelling approaches require real-time computation of reaction source terms, which is time-consuming and represents a bottleneck of turbulent combustion simulations. In order to speed up the reaction computation process, an artificial neural network (ANN) thermochemistry tabulation methodology has been proposed and developed in our previous work (Ding et al., 2021). In the present work, this methodology is further developed and applied to thermochemistry that includes NOx formation, which poses further challenges due to the small concentrations of the N-containing species. In particular, we build on the Multiple Multilayer Perceptrons (MMLP) concept, which aims to improve prediction accuracy by systematically combining multiple ANNs. A new method, MMLP-II, is proposed in this work, which trains different ANNs to predict states with different ranges of initial species concentration, in contrast to the previous MMLP-I method which trains several ANNs with different ranges of output magnitude. Both MMLP methods are applied to tabulate the complete GRI-3.0 mechanism and the resulting ANNs are tested on two different turbulent methane flames: Sandia flame D and Sydney flame SMA2. It is found that MMLP-II method can reduce the ANN error accumulation of minor species, and very accurate results are obtained in both turbulent flames. The successful application to two different turbulent combustion problems is indicative of the capacity for generalisation of the ANN tabulation approach. Finally, the reaction integration step is accelerated by a factor of about 15 with ANNs, thus rendering chemical kinetics no longer the bottleneck of the whole simulation.