This article presents a joint numerical study on the Multi Regime Burner configuration. The burner design consists of three concentric inlet streams, which can be operated independently with different equivalence ratios, allowing the operation of stratified flames characterized by different combustion regimes, including premixed, non-premixed, and multi-regime flame zones. Simulations were performed on three LES solvers based on different numerical methods. Combustion kinetics were simplified by using tabulated or reduced chemistry methods. Finally, different turbulent combustion modeling strategies were employed, covering geometrical, statistical, and reactor based approaches. Due to this significant scattering of simulation parameters, a conclusion on specific combustion model performance is impossible. However, with ten numerical groups involved in the numerical simulations, a rough statistical analysis is conducted: the average and the standard deviation of the numerical simulation are computed and compared against experiments. This joint numerical study is therefore a partial illustration of the community's ability to model turbulent combustion. This exercise gives the average performance of current simulations and identifies physical phenomena not well captured today by most modeling strategies. Detailed comparisons between experimental and numerical data along radial profiles taken at different axial positions showed that the temperature field is fairly well captured up to 60 mm from the burner exit. The comparison reveals, however, significant discrepancies regarding CO mass fraction prediction. Three causes may explain this phenomenon. The first reason is the higher sensitivity of carbon monoxide to the simplification of detailed chemistry, especially when multiple combustion regimes are encountered. The second is the bias introduced by artificial thickening, which overestimates the species' mass production rate. This behavior has been illustrated by manufacturing mean thickened turbulent flame brush from a random displacement of 1-D laminar flame solutions. The last one is the influence of the subgrid-scale flame wrinkling on the filtered chemical flame structure, which may be challenging to model.