Stable phenalenyl (PLY) radical π-dimers still play an important role for new multifunctional materials owing to their intriguing molecular structure and unusual pancake π-π bonding mode. Herein, we design a new biphenalenyl biradicaloid (1) consisting of two PLYs and one benzene ring linkage tethered by single bonds, which presents an open-shell character. Further, three π-dimers (a1, b1, and c1) combined with 1 and conventional biphenalenyl biradicaloid (a, b, and c), which are capable of forming two staggered PLY dimers, exhibiting a short interlayer distance between the monomers. Interestingly, the analysis of the frontier molecular orbital reveals that two bonding orbitals, namely, the two highest occupied molecular orbitals (HOMO and HOMO-1) are doubly occupied. The results reveal that three π-dimers display two parallel pancake bonds. Moreover, they have small diradical and tetraradical characters, large interaction energies, and strong aromaticity, which indicate the stability of these π-dimers. The present work creates a new class of strong pancake bonding and might be utilized in devising an array of materials.