The bimetallic molecular compound Dimolybdenum tetraacetate (MoMo‐Methyl) is grown on a Cu(111) surface with submonolayer coverage. Scanning tunneling microscopy experiments reveal that the compound forms two different structural phases on the Cu surface, whose ratio can be reversibly controlled by changing the sample temperature. The so‐called chain‐phase is characterized by tilted MoMo dimers bonded to the Cu surface via the methyl groups. In the so‐called mesh‐phase, on the other hand, the molecules adsorb in a flat lying adsorption configuration with one of the Mo‐atoms in direct contact with the Cu surface. Crucially, the different structural properties of the two phases reflect the different inter‐ and intramolecular interactions between the Mo metal centers, as well as the different interactions between Mo and the Cu surface atoms. In this way, the structural changes result in a modification of the cooperative effects in the system. Therefore, it is proposed that the observed reversible structural phase transition could be used to control the strength of cooperative effects in MoMo‐Methyl on Cu(111).