A macrosociological theory's central principle, suggested by Simmel's concepts of crosscutting social circles and web of group affiliations, is that intersecting social differences promote intergroup relations. This theorem is tested with data on intermarriage rates in the 125 largest metropolitan areas in the United States. Since the theorem refers to intermarriage generally, the research testing reported here analyzes measures of ten different forms of intermarriage and not only the more commonly studied ethnic intermarriage. The theorem is respecified on the basis of preliminary analysis to stipulate that multiple, not merely bivariate, intersection of social affiliations fosters intermarriage, as is, indeed, implicit in the original theoretical discussion. Eight independent empirical tests corroborate the theorem that multiple intersection of social differences furthers not merely superficial but even profound and lasting intergroup relations.