We suggest four new benzene dimers, (C6H6)(2), all featuring one or more cyclohexadiene rings trans-fused to 4- or 6-membered rings. These hypothetical dimers are 50-99 kcal/mol less stable than two benzenes, but have computed activation energies to fragmentation >27 kcal/mol. A thorough search of potential escape routes was undertaken, through cyclobutane ring cleavage to 12-annulenes, sigmatropic 1,5-H-shifts, electrocyclic ring-openings of the 6-membered rings, and Diels-Alder dimerizations. Some channels for reaction emerge, but there is a reasonable chance that some of these new benzene dimers can be made.