A search for decays of Bc+ mesons to two charm mesons is performed for the first time using data corresponding to an integrated luminosity of 3.0fb−1, collected by the LHCb experiment in pp collisions at centre-of-mass energies of 7 and 8 TeV. The decays considered are Bc+→D(s)(⁎)+D‾(⁎)0 and Bc+→D(s)(⁎)+D(⁎)0, which are normalised to high-yield B+→D(s)+D‾0 decays. No evidence for a signal is found and limits are set on twelve Bc+ decay modes.