Summary: New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., \(H_- = {\mathcal A}^{\dagger} {\mathcal A} + \alpha {\mathcal A} ^2 + \beta {\mathcal A}^{\dagger 2} \), where \(\alpha , \beta \) are real constants, with \(\alpha \neq \beta \), and \({\mathcal A}^{\dagger} \) and \({\mathcal A} \) are generalized creation and annihilation operators. It is shown that the initial Hamiltonian \(H_{-}\), and its partner \(H_{+}\), are related by pseudo supersymmetry, and they share all the eigen energies except for the ground state. This pseudo supersymmetric extension enlarges the class of non Hermitian Hamiltonians \(H_{\pm }\), related to their respective Hermitian counterparts \(h_{\pm }\), through the same similarity transformation operator \(\rho :H_{\pm } = \rho ^{-1}h_{\pm }\rho \). The formalism is applied to the entire class of shape-invariant models.