Almost all modern extensions of many-electron Symmetry-Adapted Perturbation Theory, valid up to the third-order of the perturbation expansion, have been based on one-and two-electron density matrices. Such a formalism is often called the density matrix (DM) approach. However, in 1994, Moszyński, Jeziorski, and Szalewicz introduced an alternative derivation of many-body SAPT corrections based on the second quantization formalism here referred to as the second quantization method (SQ). The formulae for the first-order exchange energy expressions presented therein are structurally very different from those of the DM formalism, but all the numerical results are identical. The SQ approach appears to be somewhat less popular than the more commonly used DM formulation. There are two known weaknesses of the SQ method that contribute to its lower popularity. Firstly, in terms of computational cost, it has slightly worse scaling with the size of the basis set due to the higher number of summations over the virtual orbitals. Secondly, the use of expressions obtained in the SQ formalism is limited only to dimer-centred basis sets. However, there are several potential advantages of this method that may make it useful in future development of SAPT. First of all, since the SQ method in the context of SAPT is based on the concept of the product of two Fermi vacuums spanned by two sets of molecular spinorbitals of the monomers A and B, the derivations of the expressions can be based on an adaptation of Wick's theorem. As a result, they can easily be automatized. Furthermore, automatic numerical implementations of the resulting expressions are also possible. Automatic derivation of second-quantized formulae has been widely used in quantum chemistry. Moreover, at the dawn of an era of quantum computing, the development of such theories is highly desirable since many quantum computing algorithms rely on encoding the fermionic creation and annihilation operators into a sequence of qubit quantum gates. In this paper, we initially concentrate on the order-by-order derivation of the general formula for corrections of arbitrary order in S, a formula which can be efficiently derived using the symbolic algebra code our group developed. We then provide a derivation of the S 4 correction in first-and second-order SAPT, showing how the second quantization approach offers an alternative way to formulate first-and second-order exchange energy. Next, we derive the exchange energies exact for all orders of the intermolecular overlap expansion that encompass contributions from all possible electron interchanges between the monomers without accounting for intramonomer correlation. Such an extension of SQ relies on the summation of a series in the S overlap matrix to infinity. We numerically test our theories on several systems that challenge the convergence with respect to S, including metal atoms and molecules possessing lone electronic pairs. This framework may be foundational for future advancements in the theory. Particularly, it might pave the way for incorporating intramolecular electron correlation effects using the coupled-cluster method or multiconfiguration methods while ensuring an accurate portrayal of exchange effects.