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In order to address the interplay of hydrogen bonding, dipolar interactions, and metal coordination, we have investigated the two-dimensional mono- and bicomponent self-assembly of three closely related diaminotriazine-based molecular building blocks and a complementary perylenetetracarboxylic diimide by means of scanning tunneling microscopy. The simplest molecular species, bis-diaminotriazine-benzene, only interacts via hydrogen bonds and forms a unique supramolecular pattern on the Au(111) surface. For the two related molecular species, which exhibit in addition to hydrogen bonding also dipolar interactions and metal coordination, the number of distinct supramolecular structures increases dramatically with the number of possible interaction channels. Deposition together with the complementary perylene species, however, always results in a single well-defined supramolecular arrangement of molecules. A detailed analysis of the observed mono- and bicomponent assemblies allows shedding light on the hierarchy of the competing interactions, with important implications for the fabrication of surface-supported supramolecular networks by design.