A flame shape bifurcation in the liquid-fueled two-stage swirled BIMER com-bustor is studied using Large Eddy Simulations. This combustor, developed at the EM2C Laboratory to study Lean Premixed Prevaporized (LPP) burners , is composed of a two-stage injection system: a central swirled pilot stage fueled with a pressure-swirl atomizer, to sustain a piloting flame, and an outer swirled stage fed with a multi-point injection, to generate the LPP regime. After ignition in the pilot-only operating condition, a V flame is stabilized near the Inner Shear Layer (ISL). When switching to multipoint-only injection, a flame shape transition is observed, and the flame bifurcates into a M-shape. In this work, we identify the mechanisms that lead to this bifurcation, and we show that the transition is driven by a complex coupling between the flame, the chamber acoustics and the ISL vortices. By switching to a multipoint-only injection, the fuel is essentially given to the ISL flame, which is mainly premixed. Because of the increased heat release and thanks to positive Rayleigh criterion, the quarter wave mode of the chamber is promoted. The ISL vortices, locked to this mode, increase in size until they are large enough to merge the flame in the CRZ, because of the radial momentum budget that forces the flow topology to switch to a bubble-like structure. Therefore, these results show that it is the existence of two possible flow topologies that renders this flame shape transition possible, the instability being responsible to transfer sufficient energy to the flow to enable the transitioning and the flame then changing its shape just to adapt to the new topology.