In our earlier paper [1], we used deformation theory to study the Painlevé equations which govern the self-similar solutions of the modified KdV (MKdV) and sinh-Gordon equations. Here we introduce a wider class of solutions of these and related equations: the multiphase similarity solutions. These are supposed to be to the standard (one-phase) similarity solutions–what multisoliton or finite-gap periodic solutions are to solitons and cnoidal waves.