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In the expression 'multi-representation', prefix and hyphen combine to promise coordination between the representations. There is more indeed to multi-representation than multiple representations. Where does the richness of multi-representation lie? How may geographical multi-representation be stored fully in the computer? This article is an attempt to answer such questions methodically, following a phenomenological approach. Starting from the concept of 'representation' itself, it appears that a representation is composed of five constituents (Phenomenon, Attention, Medium, Inscription, Reception). Multi-representation is then shown to be performed when the representations represent the same Phenomenon, and when their four other constituents are compared in turn to provide additional information on the phenomenon. Comparing involves looking for similarities, specific details, contradictions, and for what can be deduced only through the combination of the representations. In the GIS domain, phenomena are geographical, and comparisons of their representations have to be stored in the computer. But geographical phenomena are numerous and various, as well as possible computer representations: How can everything be coordinated? In view of such a demanding programme, 'GIS geographical multi-representation' appears as a vast and intricate research domain. A possible strategy is revealed as an example of methodological progression.