A strong influence of illumination and electric bias on the Curie temperature and saturation value of the magnetization is demonstrated for semiconductor structures containing a modulation-doped p-type Cd(0.96)Mn(0.04)Te quantum well placed in various built-in electric fields. It is shown that both light beam and bias voltage generate an isothermal and reversible crossover between the paramagnetic and ferromagnetic phases, in the way that is predetermined by the structure design. The observed behavior is in quantitative agreement with the expectations for systems, in which ferromagnetic interactions are mediated by the weakly disordered two-dimensional hole liquid.