We describe an optimization-based method that seeks the superposition of ligand binding cavities that maximizes their overlapping volume. Our method, called DFO-VASP, iteratively uses Boolean set operations to evaluate overlapping volume in intermediate superpositions while searching for the maximal one. Our results verify that the superpositions identified are biologically relevant, and demonstrate that DFO-VASP generally discovers cavity superpositions with similar or occasionally larger overlapping volume than those of superpositions generated with existing means.