  An experimental setup of three coupled $\mathcal{PT}$-symmetric wave guides
showing the characteristics of a third-order exceptional point (EP3) has been
investigated in an idealized model of three delta-functions wave guides in
W.~D. Heiss and G.~Wunner, J. Phys. A 49, 495303 (2016). Here we extend these
investigations to realistic, extended wave guide systems. We place major focus
on the strong parameter sensitivity rendering the discovery of an EP3 a
challenging task. We also investigate the vicinity of the EP3 for further
branch points of either cubic or square root type behavior.
