Interesting electronic properties arise in vertically stacked graphene sheets, some of which can be controlled by mutual orientation of the adjacent layers. In this study, we investigate the MBE grown multilayer graphene on Ir(111) by means of STM, LEED and XPS and we examine the influence of the substrate on the geometric and electronic properties of bilayer graphene by employing XSW and ARPES measurements. We find that the MBE method does not limit the growth to two graphene layers and that the wrinkles, which arise through extended carbon deposition, play a crucial role in the multilayer growth. We also find that the bilayer and trilayer graphene sheets have graphitic-like properties in terms of the separation between the two layers and their stacking. The presence of the iridium substrate imposes a periodic potential induced by the moiré pattern that was found to lead to the formation of replica bands and minigaps in bilayer graphene. From tight-binding fits to our ARPES data we find that band renormalization takes place in multilayer graphene due to a weaker coupling of the upper-most graphene layer to the iridium substrate.