The inclusion of exchange repulsion terms in the explicit polarization (X-Pol) model is examined by antisymmetrizing the X-Pol Hartree-product wave function; this yields XPol with full eXchange, called X-Pol-X. When the monomers are treated by Hartree-Fock theory, this calculation can be accomplished by using the formalism of block-localized wave functions (BLW) that has been used in a variety of applications. In this case the block-localized structure in the X-Pol-X wave function allows for decomposition of the full Fock matrix of a dimension of M blocks into M smaller Fock matrices. The method is illustrated by considering two trimer structures of water clusters, and it is found that the total exchange repulsion energies in these hydrogen-bonding test cases are adequately treated and-to a good approximation- are pairwise additive. We also present a formalism to yield a simplified Fock matrix by making use of the neglect of interfragment differential overlap (NIDO) approximation, which is less severe than the neglect of diatomic differential overlap (NDDO) approximation.