The possibility of a second pairing transition d --> d + is (d + id') in planar d-wave superconductors which occurs in the absence of external magnetic field, magnetic impurities, or boundaries is established in the framework of the nonperturbative phenomenon of dynamical chiral symmetry breaking: in the system of (2 + 1)-dimensional Dirac-like nodal quasiparticles. We determine the critical exponents and quasiparticle spectral functions that characterize the corresponding quantum-critical behavior and discuss some of its potentially observable spectral and transport features.