The calculation of the 3d-intrashell excitations in coordination compounds by means of the Effective Hamiltonian Crystal Field (EHCF) method is generalized to their polynuclear analogues to properly describe several open d-shells and their magnetic interactions. This challenge requires improving the precision of ca. 1000 cm(-1) to ca. 100 cm(-1) characteristic for the spin-reorientation energies. The method follows the successful EHCF paradigm, namely, the concerted usage of McWeeny's group-function approximation and Lowdin's partitioning technique, for an effective description of the multicenter d-systems. The novel approach is implemented in the MagAixTic package and validated against a series of binuclear complexes of Cr(III) featuring mu-oxygen superexchange paths. The trends in the compound series in terms of exchange constants are correctly reproduced, despite differing details of composition and structure, and the numerical results agree by order of magnitude with available experimental data and other theoretical methods.