Using proton-proton collision data, corresponding to an integrated luminosity of 9 fb(-1) collected with the LHCb detector, seven decay modes of the B-C(+) meson into a J/psi or psi(2S) meson and three charged hadrons, kaons or pions, are studied. The decays B-C (+)-> (psi(2S) -> J/psi pi(+)pi(-))pi(+), B+C -> (psi(2S)pi(+)pi(-)pi(+), B+C -> J/psi K+pi(-)pi(+) and B+C -> J/K+K-K+ are observed for the first time, and evidence for the B-C (+)-> (psi(2S)K+K-pi(+), decay is found, where J/psi and psi(2S) mesons are reconstructed in their dimuon decay modes. The ratios of branching fractions between the different B-C(+) decays are reported as well as the fractions of the decays proceeding via intermediate resonances. The results largely support the factorisation approach used for a theoretical description of the studied decays.