We investigate a layer of cobalt tetrapyridyl porphyrins (CoTPyPs) self-assembled on an almost freestanding graphene (GR) sheet supported by Ir(111) with complementary experimental techniques and density functional theory (DFT) ab initio simulations. Beside the metal atoms enclosed within the porphyrin macrocycles, additional Co atoms can be accommodated at the molecular network's interstice via physical vapor deposition and can bind up to four adjacent molecules. Therefore, such a system presents two metallic sites, both tetra-coordinated to nitrogen atoms. At the same time, a rearrangement of the network occurs depending on the coverage of such additional atoms. The bare CoTPyPs arrange themselves on GR in an almost hexagonal close-packed pattern with alternating orientations. The addition of extra Co atoms causes a dramatic transformation in the network. At full peripheral metal coverage (i.e., one additional Co per CoTPyP), the network drastically changes becoming almost square. Intermediate coverages display different peculiar patterns characterized by unique chiral structures. Importantly, our DFT calculations reveal a remarkable effect on the system's work function attributed to the presence of these additional metal atoms, despite their extremely small amount even at full coverage (less than 2% of a monolayer with respect to the number of carbon atoms in the GR sheet). Furthermore, we report a different behavior of the two Co sites showing different oxidation states and molecular orbital occupations.