Factorized Hilbert-space metrics and non-commutative quasi-Hermitian observables

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 quantum models in which these plus the underlying physical Hilbert-space metric $\Theta$ are all represented terms auxiliary operator $(N+1)-$plet $Z_k$, $k=0,1,\ldots,N$. Our formalism degenerates to ${\cal PT}-$symmetric mechanics at $N=2$, $\Theta=Z_2Z_1$, parity P}=Z_2$, charge C}=Z_1$ and Hamiltonian $H=Z_0$.