The complex interplay between superconducting and magnetic phases remains poorly understood. Here, we report on the phase separation of doped holes into separate magnetic and superconducting regions in superoxygenated La(2-x)Sr(x)CuO(4+y), with various Sr contents. Irrespective of Sr-doping, excess oxygen raises the superconducting onset to 40 K with a coexisting magnetic spin-density wave that also orders near 40 K in each of our samples. The magnetic region is closely related to the anomalous, 1/8-hole-doped magnetic versions of La(2)CuO(4), whereas the superconducting region is optimally doped. The two phases are probably the only truly stable ground states in this region of the phase diagram. This simple two-component system is a candidate for electronic phase separation in cuprate superconductors, and a key to understanding seemingly conflicting experimental observations.