  A broad family of phase transitions in the closed as well as open quantum
systems is known to be mediated by a non-Hermitian degeneracy (a.k.a.
exceptional point, EP) of the Hamiltonian. In the EP limit, in general, the
merger of an $N-$plet of the energy eigenvalues is accompanied by a parallel
(though not necessarily complete) degeneracy of eigenstates (forming an
EP-asociated $K-$plet; in mathematics, $K$ is called the geometric multiplicity
of the EP). In the literature, unfortunately, only the benchmark matrix models
with $K=1$ can be found. In our paper the gap is filled: the EP-mediated
quantum phase transitions with $K>1$ are called "clustered", and a family of
benchmark models admitting such a clustering phenomenon is proposed and
described. For the sake of maximal simplicity our attention is restricted to
the real perturbed-harmonic-oscillator-type N by N matrix Hamiltonians which
are exactly solvable and in which the perturbation is multiparametric (i.e.,
maximally variable) and antisymmetric (i.e., maximally non-Hermitian). A
labeling (i.e., an exhaustive classification) of these models is provided by a
specific partitioning of N.
