We have demonstrated that arbitrary order permutation operator of 2n electrons between monomers can be straightforwardly obtained by consecutively multiplying a single-pair permutation operator P 2 and selecting the part proportional to S 2n . This operator possesses a normal-order form relative to a product of physical vacuums for monomers A and B. Furthermore, we developed a symbolic algebra program to automatically derive tensor formulae for S 4 exchange components of SAPT in the first-and second order. The automatic implementation was conducted using the Psi4numpy suite of codes. The new toolbox we have developed enables us to customize the SAPT framework in theories extending beyond the single-determinant wave function, thereby broadening applicability of SAPT. For instance, cluster amplitudes can be effortlessly incorporated into such a framework.