A modular extension of Arg-tuProlog, a light-weight argumentation tool, is here presented and discussed, highlighting how it enables reasoning with rules and interpretations of multiple legal systems. Its effectiveness is demonstrated with examples from different national private international law (PIL) laws, running in Arg-tuProlog. PIL addresses overlaps and conflicts between legal systems by distributing cases between the authorities of such systems (jurisdiction) and establishing what rules these authorities have to apply to each case (choice of law).