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 $\alpha \neq \beta$, and ${\cal{A}}^{\dagger}$ and ${\cal{A}}$ 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.