  It is well known that an (in general, non-commutative) set of non-Hermitian
operators $\Lambda_j$ with real eigenvalues need not necessarily represent
observables. We describe a specific class of quantum models in which these
operators plus the underlying physical Hilbert-space metric $\Theta$ are all
represented in terms of an auxiliary operator $(N+1)-$plet $Z_k$,
$k=0,1,\ldots,N$. Our formalism degenerates to the ${\cal PT}-$symmetric
quantum mechanics at $N=2$, with metric $\Theta=Z_2Z_1$, parity ${\cal P}=Z_2$,
charge ${\cal C}=Z_1$ and Hamiltonian $H=Z_0$.
