Can we predict electronic bands beyond DFT across different systems? A material’s electronic band structure provides the basis for band gaps, densities of states, and carrier effective masses, while connecting theory with spectroscopy. For quantum materials, getting these bands right can change our understanding of physics. Yet the calculations needed to go beyond standard DFT remain expensive. We introduce O-krystal, a periodic E(3)-equivariant graph neural network that learns corrections to individual electronic states. It uses orbital information from lower cost PBE calculations in both real and reciprocal space, bringing local electronic interactions and the momentum dependence of the crystal into the same model. O-kRystal is the first machine learning framework to combine: 1. Scale across chemistry: HSE06 band predictions across nearly 6,000 chemically diverse three dimensional materials 2. Breadth across electronic behavior: metals and insulators, magnetic and nonmagnetic systems, with spin resolution and different numbers of bands 3. Flexibility across theory and dimensionality: the same framework, trained separately, predicts G0W0 quasiparticle energies in two dimensional materials. Although trained only at high symmetry points, it maintains comparable accuracy at unseen points along band paths and reconstructs densities of states from dense Brillouin zone predictions. On a separate benchmark of strongly correlated materials, O-kRystal reduces the PBE band energy MAE by 68.7%. As demonstrated for AFM-II MnO, a canonical Mott insulator, it captures distinct corrections to Mn 3d and O 2p states, recovering their relative placement by accounting for the effects of exact exchange. As electronic structure methods advance, this framework offers a path toward experimental accuracy and large-scale discovery of quantum materials with emergent phases, including superconductivity. @Caltech