  A family of non-Hermitian but ${\cal PT}-$symmetric $2J$ by $2J$ toy-model
tridiagonal-matrix Hamiltonians $H^{(2J)}=H^{(2J)}(t)$ with $J=K+M=1,2,\ldots$
and $t<J^2$ is studied, for which a real but non-Hermitian $2K$ by $2K$
tridiagonal-submatrix component $C(t)$ of the Hamiltonian is assumed coupled to
its other two complex but Hermitian $M$ by $M$ tridiagonal-submatrix components
$A(t)$ and $B(t)$. By construction, (i) all of the submatrices get decoupled at
$t=t_M=M\,(2J-M)$ with $M=1,2,\ldots,J$; (ii) at all of the parameters $t=t_M$
with $M=J-K=0,1,\ldots,J-1$ the Hamiltonian ceases to be diagonalizable
exhibiting the Kato's exceptional-point degeneracy of order $2K$; (iv) the
system's ${\cal PT}-$symmetry gets spontaneously broken when $t\leq
t_{J-1}=J^2-1$.
