Pseudo supersymmetric partners for the generalized Swanson model

New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., $ H_- = {\cal{A}}^{\dagger} {\cal{A}} + \alpha {\cal{A}} ^2 + \beta {\cal{A}}^{\dagger 2} $,where$ \alpha \beta $ are real constants, with $\alpha \mathrm{\ne }\beta$, and ${\mathcal{A}}^{†}$ 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.