The adsorption of trimesic acid (TMA) on Cu(110) has been studied in the temperature range between 130 and 550 K and for coverages up to one monolayer. We combine scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), reflection absorption infrared spectroscopy (RAIRS), X-ray photoemission spectroscopy (XPS), and density functional theory (DFT) calculations to produce a detailed adsorption phase diagram for the TMA/Cu(110) system as a function of the molecular coverage and the substrate temperature. We identify a quite complex set of adsorption phases, which are determined by the interplay between the extent of deprotonation, the intermolecular bonding, and the overall energy minimization. For temperatures up to 280 K, TMA molecules are only partly deprotonated and form hydrogen-bonded structures, which locally exhibit organizational chirality. Above this threshold, the molecules deprotonate completely and form supramolecular metal-organic structures with Cu substrate adatoms. These structures exist in the form of single and double coordination chains, with the molecular coverage driving distinct phase transitions.