The Darmstadt Multi-Regime Burner (MRB) is modelled using a multi-modal manifold-based combustion model with Large Eddy Simulation (LES). The MRB26b operating condition is chosen due to its multi-regime behaviour. The multi-modal combustion model is implemented using the In-Situ Adaptive Manifolds (ISAM) computational approach, combining a two-dimensional multi-modal manifold solver in mixture fraction and generalised progress variable with In-Situ Adaptive Tabulation (ISAT). While previous studies using the multi-modal manifold model showcased its potential to be applied to multi-regime combustion problems, the current study extends the model framework by including a non-linear generalised progress variable definition , which ensures exact recovery of the non-premixed combustion limit and consideration of the cross-scalar dissipation rate. Mean and RMS quantities are compared with experimental data, demonstrating accurate capturing of the multi-regime flame structure. The analysis includes scatter plots of key species (CO and H2), known indicators for multi-regime combustion, and are used to discuss deviations from the traditional uni-manifold methods based on premixed combustion. The effect of the inclusion of the mixture fraction dissipation rate χ ZZ is quantified by comparing one-dimensional (in generalised progress variable) and two-dimensional manifold solutions at the same generalised progress variable dissipation rates. Larger deviations from premixed combustion occur at higher values of χ ZZ and states closer to chemical equilibrium. The region influenced by χ ZZ is determined geometrically and was found to be close to the inlets. The multi-modal manifold implemented with ISAM is demonstrated to be an attractive alternative to conventional tabulated chemistry methods using premixed or non-premixed flamelets for handling multi-regime combustion problems with minimal impact on the computational cost.