Chemical bonding interactions are the main driving force for the formation of molecules and materials from atoms. The two-electron/multicenter pancake π-π bonding found in phenalenyl (PLY, 1) radical π-dimers is intriguing due to its unconventional nature of covalent bonding for molecular aggregations and its propensity to induce unique optical, electronic, and magnetic properties. By using high-level quantum chemistry calculations, we show that the B- or N-doped PLYs (2 and 4), usually considered closed-shell and therefore trifling, can be rendered open-shell singlet by proper edge substitutions (3 and 5). The resulting two unpaired valence electrons on each molecular unit contribute to the formation of a genuine pancake-shaped 4e/all-sites double π-π bonding upon intermolecular π-dimerization, in contrast to the 2e/half-sites single π-π bonding in the parent PLY π-dimers. The unusual double π-π bonding motif discovered in these PLY analogues may broaden the landscape of, and find new applications for, intermolecular covalent bonding interactions.