All previous cuprate superconductors display a set of common features: (i) vicinity to a Cu 3d 9 configuration; (ii) separated CuO2 planes; (iii) superconductivity for doping δ ∼ 0.1−0.3. Recently [PNAS 24, 12156 (2019)] challenged this picture by discovering "highly overdoped" superconducting Ba2CuO3+y. Using density-functional theory + dynamical mean-field theory, we reveal a bilayer structure of Ba2CuO3.2 of alternating quasi 2D and quasi 1D character. Correlations tune an interlayer self-doping leading to an almost half-filled, strongly nested quasi 1D d b 2 −c 2 band, which is prone to strong antiferromagnetic fluctuations, possibly at the origin of superconductivity in Ba2CuO3+y.