A Lewis acid-catalyzed formal (3+3)-cycloaddition of bicyclo[1.1.0]butane carboxylates with protected aziridines has been developed using Sc(OTf)₃ under mild conditions, enabling efficient access to 2-azabicyclo[3.1.1]heptanes. Acid-catalyzed dimerization of bicyclobutanes (BCBs) has been studied in detail. The process yields four distinct dimeric scaffolds, categorized as cyclobutene- or cyclobutane-embedded dimers. These arise via (3+2)- or (3+3)-cycloaddition of an unusual 1,3-dipole with cyclobutene or bicyclobutane respectively. We developed an efficient iterative synthetic strategy employing two successive oxidative steps for the construction of complex polycyclic aromatic scaffolds from dimethylnaphthalene precursors.