Strengthened PT-symmetry with P≠Pâ€

In quantum mechanics working with non-Hermitian PT-symmetric Hamiltonians (i.e., with an indefinite metric P in Hilbert space) we propose to relax the usual constraint P=P†. We show that this merely induces certain “hidden” symmetries responsible, say, for the degeneracy of levels. Using a triplet of the coupled square wells for illustration we show that the bound states may remain stable in a large domain of couplings.