  Non-Hermitian systems distinguish themselves from Hermitian systems by
exhibiting a phase transition point called an exceptional point (EP), which is
the point at which two eigenstates coalesce under a system parameter variation.
Many interesting EP phenomena such as level crossings/repulsions in
nuclear/molecular and condensed matter physics, and unusual phenomena in optics
such as loss-induced lasing and unidirectional transmission can be understood
by considering a simple 2x2 non-Hermitian matrix. At a higher dimension, more
complex EP physics not found in two-state systems arises. We consider the
emergence and interaction of multiple EPs in a four-state system theoretically
and realize the system experimentally using four coupled acoustic cavities with
asymmetric losses. We find that multiple EPs can emerge and as the system
parameters vary, these EPs can collide and merge, leading to higher order
singularities and topological characteristics much richer than those seen in
two-state systems.
