The growth of nearly full coverage of multilayer graphene on the surface of a 99.8% purity copper foil has been experimentally studied. It has been shown that the film thickness can be controlled by a single parameter, the growth time, and growth can be extended until nearly full coverage of more than one layer graphene over the copper surface. The results are supported by scanning electron microscopy and Raman analysis together with optical transmittance and sheet resistance measurements. It has been verified that silicon oxide impurity particles within the copper act as catalysts and the seeds of multilayer graphene islands. The linear increase of the average thickness of graphene to the growth time has been attributed to the interplay between the mean distance between the impurities on the surface and the molecular mean free path in the process gas. A qualitative model is proposed to explain the microscopic mechanism of the multilayer growth on copper. These results contribute to the understanding of the chemical vapour deposition growth kinetics towards the objective of large area high quality graphene production with tuneable layer thickness.