  Nontrivial spectral properties of non-Hermitian systems can lead to
intriguing effects with no counterparts in Hermitian systems. For instance, in
a two-mode photonic system, by dynamically winding around an exceptional point
(EP) a controlled asymmetric-symmetric mode switching can be realized. That is,
the system can either end up in one of its eigenstates, regardless of the
initial eigenmode, or it can switch between the two states on demand, by simply
controlling the winding direction. However, for multimode systems with
higher-order EPs or multiple low-order EPs, the situation can be more involved,
and the ability to control asymmetric-symmetric mode switching can be impeded,
due to the breakdown of adiabaticity. Here we demonstrate that this difficulty
can be overcome by winding around exceptional curves by additionally crossing
diabolic points. We consider a four-mode $\cal PT$-symmetric bosonic system as
a platform for experimental realization of such a multimode switch. Our work
provides alternative routes for light manipulations in non-Hermitian photonic
setups.
