  The phenomenon of degeneracy of an $N-$plet of bound states is studied in the
framework of quantum theory of closed (i.e., unitary) systems. For an
underlying Hamiltonian $H=H(\lambda)$ the degeneracy occurs at a Kato's
exceptional point $\lambda^{(EPN)}$ of order $N$ and of the spectral geometric
multiplicity $K<N$. In spite of the phenomenological appeal of the concept
(tractable as a quantum phase transition, or as a unitary processes of the loss
of the observability of the system), the dedicated literature deals,
predominantly, just with the models where $N=2$ and $K=1$. In our paper it is
shown that the construction of the $N>2$ and $K>1$ benchmark models of the
process of degeneracy becomes feasible and non-numerical for a broad class of
specific, maximally non-Hermitian anharmonic-oscillator toy-model Hamiltonians.
An exhaustive classification of non-equivalent processes is given by a
partitioning of the unperturbed spectrum into equidistant and centered
unperturbed subspectra.
