A bstract Using proton-proton collision data, corresponding to an integrated luminosity of 9 fb − 1 collected with the LHCb detector, seven decay modes of the $$ {\mathrm{B}}_{\mathrm{c}}^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math> meson into a J / ψ or ψ(2S) meson and three charged hadrons, kaons or pions, are studied. The decays $$ {\mathrm{B}}_{\mathrm{c}}^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math> → (ψ(2S) → J / ψπ + π − )π + , $$ {\mathrm{B}}_{\mathrm{c}}^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math> → ψ(2S)π + π − π + , $$ {\mathrm{B}}_{\mathrm{c}}^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math> → J / ψK + π − π + and $$ {\mathrm{B}}_{\mathrm{c}}^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math> → J / ψK + K − K + are observed for the first time, and evidence for the $$ {\mathrm{B}}_{\mathrm{c}}^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math> → ψ(2S)K + K − π + , decay is found, where J / ψ and ψ(2S) mesons are reconstructed in their dimuon decay modes. The ratios of branching fractions between the different $$ {\mathrm{B}}_{\mathrm{c}}^{+} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>+</mml:mo></mml:msubsup></mml:math> 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.