Novel imaging methods show that the mobile dopants in optimum doped La2CuO4+y (LCO) get self-organized, instead of randomly distributed, to form an inhomogeneous network of nanoscale metallic puddles with ordered oxygen interstitials interspersed with oxygen-depleted regions. These puddles are expected to be metallic, being far from half filling because of high dopant density, and to sustain superconductivity having a size in the range 5–20 nm. However, the electronic structure of these heavily doped metallic puddles is not known. In fact the rigid-band model fails because of ordering of dopants and supercell calculations are required to obtain the Fermi surface reconstruction.We have performed advanced band calculations for a large supercell La16Cu8O32+N where N = 1 or 2 oxygen interstitials form rows in the spacer La16O16+N layers intercalated between the CuO2 layers as determined by scanning nano x-ray diffraction. The additional occupied states made by interstitial oxygen orbitals sit well below the Fermi level (EF ) and lead to hole doping as expected. The unexpected results show that in the heavily doped puddles the altered Cu(3d)-O(2p) band hybridization at EF induces a multiband electronic structure with the formation of multiple Fermi surface spots: (a) Small gaps appear in the folded Fermi surface, (b) three minibands cross EF with reduced Fermi energies of 60, 150, and 240 meV, respectively, (c) the density of states and band mass at EF show substantial increases, and (d) spin-polarized calculations show a moderate increase of antiferromagnetic spin fluctuations. All calculated features are favorable to enhance superconductivity; however, the comparison with experimental methods probing the average electronic structure of cuprates will require the description of the electronics of a network of multigap superconducting puddles.