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. Plays a central role in catabolism of lysine, hydroxylysine, and tryptophan, by transporting common metabolite intermediates (such as 2-oxoadipate) into the mitochondria, where it is converted into acetyl-CoA and can enter the citric acid (TCA) cycle. 2-oxoadipate(in) + 2-oxoglutarate(out) = 2-oxoadipate(out) + 2-oxoglutarate(in) 2-oxoglutarate(out) + hexanedioate(in) = 2-oxoglutarate(in) + hexanedioate(out) 2-oxoglutarate(out) + L-2-aminoadipate(in) = 2-oxoglutarate(in) + L-2-aminoadipate(out) 2-oxoglutarate(out) + glutarate(in) = 2-oxoglutarate(in) + glutarate(out) 2-oxoglutarate(out) + 2-oxoheptanedioate(in) = 2-oxoglutarate(in) + 2-oxoheptanedioate(out) 2-oxoglutarate(out) + heptanedioate(in) = 2-oxoglutarate(in) + heptanedioate(out) 2-oxoglutarate(out) + citrate(in) = 2-oxoglutarate(in) + citrate(out) Belongs to the mitochondrial carrier (TC 2.A.29) family.