Summary: We consider the infinite-range \(XY\) spin glass in the presence of a \(p\)-fold anisotropy parameter \(D_p\), favouring \(p\) orientations in a plane. This model interpolates between the \(XY\) \((D_p \to 0)\) and \(p\)-state clock \((D_p \to \infty)\) spin glasses. For \(p \geq 4\), \(D_p\) is irrelevant in what concerns the qualitative behaviour of the Parisi function. Special attention is devoted to the \(p=3\) case, for which the replica-symmetry-breaking scheme leads to very distinct order-parameter functions in the two end-point limits. We analyse the evolution of the Parisi function for varying \(D_3\) and find two distinct crossovers in its shape. We evaluate the anisotropy parameter \((D^*_3)\) at the crossover and find that the Parisi function changes from its conventional behaviour (continuous and monotonically increasing), typical of the \(XY\) spin glass \((D_3<D^*_3)\), to the step function characteristic of Potts spin glasses \((D_3 \geq D^*_3)\).