Transports dicarboxylates across the inner membranes of mitochondria by a counter-exchange mechanism.Can transport 2-oxoadipate (2-oxohexanedioate), 2-oxoglutarate, adipate (hexanedioate), glutarate, and to a lesser extent, pimelate (heptanedioate), 2-oxopimelate (2-oxoheptanedioate), 2-aminoadipate (2-aminohexanedioate), oxaloacetate, and citrate.