As a typical electron deficient element, beryllium is potentially suitable for designing the species with novel non-classical planar hypercoordinate carbon due to high preference for the planar structures by small  beryllium-containing clusters. In particular, the CBe₅^4– cluster with a planar pentacoordinate carbon (ppC) had been proved by many previous studies to be an excellent template structure for the systematic design of ppC species through attaching various monovalent atoms on the bridging position of Be–Be edges. In this work, based on the analysis and extension on our recently reported CBe₄M_n^n–2 (M = Li, Au, n = 1～3) species, we propose that ptC  cluster CBe₄^2– is similar to CBe₅^4– in that it can also be employed as a template structure to systematically design the ptC species through binding various monovalent atoms on the bridging position of Be–Be edges. Our extensive screening suggests that the feasible bridging atoms (E) can be found in group 1 (H, Li, Na), group 11 (Cu, Ag, Au), and group 17 (F, Cl, Br, I) elements, leading to total thirty eligible ptC species with CBe₄ core moiety (CBe₄E_n^n–2). The ptC atoms in these species are involved into three delocalized s  bonds and a delocalized p bond, thereby not only obeying the octet rule, but also possessing novel 6s +2p double aromaticity, which significantly stabilizes the ptC arrangement. In addition, the attached bridging atoms can stabilize the CBe₄ core ptC moiety by replacing the highly diffused Be–Be two-center two-electron bonds with the much less diffused Be–E two-center two-electron bonds or Be–E–Be three-center two-electron bonds, as reflected by the increasing HOMO-LUMO gaps when the number of bridging atoms increases. Remarkably, the stochastic search algorithm in combination with high level CCSD(T) calculations revealed that twenty-six of the thirty-one ptC species (including previously reported six species) were global energy minima on their corresponding potential energy surfaces, in which twenty-five of them were also confirmed to be dynamically viable. They are suitable for the generation and characterization in gas phase experiments and followed spectroscopic studies.