Dynamical parametric encirclement around an Exceptional Point (EP) and corresponding asymmetric state transfer phenomenon have attracted considerable attention recently. In this context, beyond the reported time-asymmetric state dynamics around a second-order EP (EP2) in a two-level system, the investigation of similar state dynamics around a third-order EP (EP3) in a multi-state system, having comparably complex topology with rich physics, is lacking. Here, we report a fabrication-feasible few-mode supported planar optical waveguide with a customized gain–loss profile and investigate the effect of dynamical parametric encirclement around an EP3 in the presence of multiple EP2s. The cube-root branch point behaviour is established in terms of successive switching between the propagation constants of the coupled modes following an adiabatic encirclement process. Now, while considering the dynamical encirclement process, the breakdown in system adiabaticity around an EP3 leads to a unique light dynamics, where we have shown the breakdown of chirality of the device. © 2020 Elsevier B.V.