rnThe simple BssE-free SCF method (CHA/F) introduced in the previous parts of this series is extended to the case of three subsystems, which may be either three weakly interacting molecules or a bimolecular system described by using bond functions. The CHA/F formalism is formulated in a more transparent manner, indicating also a straightforward way for generalization to the case of an arbitrary number of subsystems. The illustrative calculations show the viability of using the CHA/F scheme for three-component systems.