In this study, we investigate the peculiar coverage dependent supramolecular arrangement of 2H-tetraphenylporhpyrin (2HTPP) on Cu(111) with scanning tunneling microscopy at room-temperature. At low coverage, "slow" diffusion of individual 2HTPP molecules along the close-packed atomic rows of the substrate is observed, and no supramolecular ordering occurs. However, at higher coverage, the formation of ordered, checkerboard-like domains is found, with two molecules per unit cell at different distances from the surface. This behavior is attributed to a complex interplay of site specific molecule-substrate interaction, mainly the strong interaction between the iminic N atoms and Cu substrate atoms, with intermolecular T-type and pi-pi interactions.