Owing to the worldwide shortage of deceased-donor organs for transplantation, living donations have become a significant source of transplant organs. However, not all willing donors can donate to their intended recipients because of medical incompatibilities. These incompatibilities can be overcome by an exchange of donors between patients. For kidneys, such exchanges have become widespread in the last decade with the introduction of optimization and market design techniques to kidney exchange. A small but growing number of liver exchanges have also been conducted. Over the last two decades, a number of transplantation procedures emerged where organs from two living donors are transplanted to a single patient. Prominent examples include dual-graft liver transplantation, lobar lung transplantation, and simultaneous liver-kidney transplantation. Exchange, however, has been neither practiced nor introduced in this context. We introduce dual-donor organ exchange as a novel transplantation modality, and through simulations show that living-donor transplants can be significantly increased through such exchanges. We also provide a simple theoretical model for dual-donor organ exchange and introduce optimal exchange mechanisms under various logistical constraints.