Multi-regime turbulent combustion modelling remains challenging and is explored with occurrence of local extinction in this study. A partially premixed model based on unstrained premixed flamelets is used in this work to investigate a piloted jet flame configuration with inhomogeneous inlets. Three different cases are simulated, which differ in the bulk mean velocity that amounts respectively to about 50%, 70% and 90% of the blow off velocity measured experimentally. As the jet velocity approaches the blow off limit, local extinctions start to occur along the flame surface and thus these flames are challenging from a modelling prospective. Two different numerical approaches, involving scaled and unscaled progress variable respectively, are compared to elucidate their abilities and limitations to predict local extinctions and to deal with the three-stream problem at the pilot/coflow interface. The key modelling details for such predictions are indicated and discussed. LES results are systematically compared to two sets of experimental measurements available in the literature for the three flames. The differences observed in the two experimental datasets are also discussed with the help of LES results. Although both approaches show promising agreement for the flame statistics, the scaled progress variable approach better predicts the local extinctions. The unscaled approach shows to naturally handle the three-stream problem without additional treatment for the pilot/coflow interface, which is required for the scaled approach. Furthermore, computed scalar dissipation rate of mixture fraction is compared with the measurements showing good agreement for the conditions investigated. This further suggests that local extinctions can be predicted using unstrained flamelets if the correct scalar mixing and its dissipation are captured.