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In a recent paper a pair of operators $a$ and $b$ satisfying the equations$a^\dagger a=bb^\dagger+\gamma\1$ and $aa^\dagger=b^\dagger b+\delta\1$, hasbeen considered, and their nature of ladder operators has been deduced andanalysed. Here, motivated by the spreading interest in non self-adjointoperators in Quantum Mechanics, we extend this situation to a set of fouroperators, $c$, $d$, $r$ and $s$, satisfying $ dc=rs+\gamma\1$ and$cd=sr+\delta\1$, and we show that they are also ladder operators. We showtheir connection with biorthogonal families of vectors and with the so-called$\D$-pseudo bosons. Some examples are discussed.

Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra