A combined density and density-matrix functional method is proposed for the calculation of potential energy curves of molecular multibond dissociation. Its density-matrix part, a pair-density functional, efficiently approximates the ab initio pair density of the complete active space (CAS) method. The corresponding approximate on-top pair density Π is employed to correct for double counting in the correlation energy functional. The proposed ELS+ method, which augments the extended Löwdin-Shull (ELS) density-matrix functional with the Π-based scaled density functional, closely reproduces potential curves of the paradigmatic multibond dissociation in N2, H2O, and H2CO molecules calculated with the recently proposed CASΠDFT [CAS augmented with the Π-based scaled correlation correction of density functional theory (DFT)] method. Furthermore, with the additional correction for the intrafragment correlation between the broken-bond electrons, ELS++ reproduces well the benchmark potential curve of the N2 molecule by Lie and Clementi.