Within this work we have discussed size-consistent, sizeextensive and regular extensions to the BW-s2 partitioning. By dissecting the underlying mathematical requirements for these extensions and considering the structure of the manifold of all possible extensions, we have come to the conclusion that there generally exists an uncountable number of BW-s2 theories. In order to make these theories accessible, we propose an algorithm that incorporates the linear span of one-body operators which can be built from physically meaningful tensor components. Additionally, we have created an automated procedure for this generation. Truncating the resulting regulariser such that it includes only terms up to quadratic order in the wavefunction amplitudes, we determined a general regularisation operator with 29 parameters. The compute cost of this procedure scales the same way with molecular size and atomic orbital basis set size as MP2 theory, apart from requiring iterations regardless of orbital representation. Lastly, we considered examples with analytical solutions to determine conditions of exactness for the proposed parameter set. In particular, an element of strong correlation can be captured in BW-s2 by ensuring exactness for H 2 at dissociation in a minimal basis. [ Ĥ(0) ] FIG. . Diagram for the construction of the exact zeroth order Hamiltonian.