Two-component or two-channel superconductivity has been proposed since long to be a source of raising the superconducting transition temperature T-c considerably. The first observation of two-component superconductivity was made in Nb-doped SrTiO3, yet without the hope for T-c enhancement. An unambiguous observation of two superconducting gaps has been made in the recently discovered high-T-c compound MgB2 where the two component interband interaction amplifies T-c by a factor of 1.6 as compared to a single band system. Another candidate for such a scenario has been speculated to be verified in the cuprate superconductors, but the overwhelming experimental evidence for a d-wave order parameter in the CuO2 planes has largely suppressed this aspect. Here it is shown that the coexistence of an s-wave and d-wave order parameter in cuprates is a scenario in which the observed high T(c)s can be realized. The crucial quantity is here the pairwise exchange interaction of holes between the two channels caused by quantum interference. Lattice effects on superconductivity are explicitly incorporated and shown to be of major relevance to superconductivity including various exotic isotope effects. (C) 2004 Elsevier B.V. All rights reserved.