We review and extend a previous study(1) on the symmetry of the superconducting state, stimulated by recent tunneling and Andreev reflection measurements giving robust evidences for the existence of a d(x2-y2) + id(xy) order parameter in the overdoped regime of two different cuprates. Looking for a possible second-order phase transition from a standard d(x2-y2) to a mixed and time reversal breaking state, we confirm the results of our previous analysis on La2-xSrxCuO4. In the case of Y1-yCayBa2Cu3O7-x as well, among all the allowed symmetries, the d(x2-y2) + id(xy) is the most favored one and the unconventional state is likely to occur in a small dome of the phase diagram located in the optimal-overdoped region and at very low temperatures. RI Capone, Massimo/A-7762-2008