The adsorption of metal-phthalocyanine (MPc) layers (M = Fe, Co, Cu) assembled on graphene/Ir(111) is studied by means of temperature-programmed X-ray photoemission spectroscopy (XPS) and near-edge X-ray absorption fine structure (NEXAFS). The balance between interaction forces among the organometallic molecules and the underlying graphene gives rise to flat-lying molecular layers, weakly interacting with the underlying graphene. Further MPc layers pile up face-on onto the first layer, up to a few nanometers thickness, as deduced by NEXAFS. The FePc, CoPc, and CuPc multilayers present comparable desorption temperatures, compatible with molecule-molecule interactions dominated by van der Waals forces between the π-conjugated macrocycles. The MPc single layers desorb from graphene/Ir at higher temperatures. The CuPc single layer desorbs at lower temperature than the FePc and CoPc single layers, suggesting a higher adsorption energy of the FePc and CoPc single layers on graphene/Ir with respect to CuPc, with increasing molecule-substrate interaction in the order E(CuPc) < E(FePc) ~ E(CoPc).