  Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians
describing open quantum or wave systems have a variety of potential
applications in particular in optics and photonics. However, the experimental
realization is notoriously difficult. Recently, Q. Zhong et al. [Phys. Rev.
Lett. 125, 203602 (2020)] have introduced a robust construction where a
unidirectional coupling of two subsystems having exceptional points of the same
order leads generically to a single exceptional point of twice the order. Here,
we investigate this scheme in a different manner by exploiting the nilpotency
of the traceless part of the involved Hamiltonians. We generalize the scheme
and derive a simple formula for the spectral response strength of the composite
system hosting a higher-order exceptional point. Its relation to the spectral
response strengths of the subsystems is discussed. Moreover, we investigate
nongeneric perturbations. The results are illustrated with an example.
