  Bound states generated by K coupled PT-symmetric square wells are studied in
a series of models where the Hamiltonians are assumed $R-$pseudo-Hermitian and
$R^2-$symmetric. Specific rotation-like generalized parities $R$ are considered
such that $R^N=I$ at some integers N. We show that and how our assumptions make
the models exactly solvable and quasi-Hermitian. This means that they possess
the real spectra as well as the standard probabilistic interpretation.
