We demonstrate the supramolecular and structural equivalence of two halogen-bond donors (I and Br) and three acceptors (O, NH and S) through the synthesis of seven isostructural halogen-bonded cocrystals, involving six different molecules: 1,4-dibromo- and 1,4-diiodotetrafluorobenzene (donors) and thiomorpholine, thioxane, morpholine, and piperazine (acceptors). The formation of isostructural cocrystals indicates how cocrystallization may be used to overcome shape and functional group dissimilarities that control molecular arrangement in the solid state. The differences in composition between the seven isostructural cocrystals directly affect the strength and nature of halogen bonds between their constituents, allowing the systematic variation of cocrystal physical properties, in particular the melting point, without affecting their crystal structure. Replacement of each O or S halogen-bond acceptor with an NH group provided an approximate 70 degrees C increase in melting point, whereas the replacement of I with Br as the halogen-bond donor lowered the melting point of the resulting solid by a similar amount.