We study experimentally the behaviour of magnesium Rydberg series converging to the Mg+(3s) and Mg+(3p) ion states, coupled by a strong (I  1012 Wcm-2) light field that is resonant with the transition between the ion states (l  280 nm). This strong-field version of isolated-core excitation leads to modifications in the photoionization spectrum of the bound Rydberg series and to transitions between bound Rydberg states when the Rabi frequency associated with the core transition becomes larger than the Rydberg spacing.