We use cryogenic scanning tunneling microscopy and spectroscopy and density-functional theory calculations to inspect the modulation of electronic states of aromatic molecules. The molecules are selfassembled on a Cu(111) surface forming molecular networks in which the molecules are in different contact configurations, including laterally coupled to different numbers of coordination bonds and vertically adsorbed at different heights above the substrate. We quantitatively analyze the molecular states and find that a delocalized empty molecular state is modulated by these multiple contacts in a cooperative manner: its energy is down shifted by $0:16 eV for each additional lateral contact and by $0:1 eV as the vertical molecule-surface distance is reduced by 0.1 Å in the physisorption regime. We also report that in a moleculemetal-molecule system the bridging metal can mediate the electronic states of the two molecules. DOI: 10.1103/PhysRevLett.110.046802 PACS numbers: 73.20.Hb, 68.37.Ef, 73.63.Rt, 85.65.+h The electronic structure of a molecule is subject to the coupling of the molecule with its environment [1,2]. A thorough understanding of this issue is of great importance in the field of molecular electronics considering that the characteristics of molecular devices are determined by the molecular electronic structures and their contacts [3]. For example, a metal-molecule interface may strongly modify the molecular orbitals, and consequently, molecular conductance [3]. As one of the ultimate goals of molecular electronics is to realize single-molecule devices, wherein single molecules are connected to electrodes, one needs to understand how molecule-electrode coupling affects the molecular electronic structures at the level of individual molecules. Scanning tunneling microscopy and spectroscopy (STM-STS) have been used to address this challenging problem owing to their capability of resolving geometric details of molecule-metal contacts and simultaneously measuring the single-molecule electronic properties. These studies revealed in great detail that the molecular frontier orbitals are modulated when the molecules are coupled to metal atoms or a metal substrate [4][5][6][7][8][9][10][11][12][13][14]. So far, most of these studies focused on molecules coupled to one or at most two metal contacts. In future single-molecule devices, however, the molecules will be mostly connected to multiple electrodes, for example, to source, drain and gate electrodes in a field-effect transistor [15][16][17][18][19][20]. It is highly desirable to study individual molecules that are coupled to multiple metal contacts.In this Letter, we report on a combined study with low-temperature STM-STS and density-functional theory (DFT) of the electronic structures of extended aromatic molecules that are coupled with multiple metal contacts. The molecules are attached laterally to two or three neighboring molecules through metal-ligand coordination bonds and vertically to a metal surface at different distance. These parameters can be se...