A bstract Four decay modes of the $$ {B}_c^{+} $$ <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 meson and multiple charged kaons or pions are studied using proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV and corresponding to an integrated luminosity of 9 fb − 1 . The decay $$ {B}_c^{+} $$ <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 − π + π + π − is observed for the first time, and evidence for the $$ {B}_c^{+} $$ <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/ψ 4 π + 3 π − decay is found. The decay $$ {B}_c^{+} $$ <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/ψ 3 π + 2 π − is observed and the previous observation of the $$ {B}_c^{+} $$ <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 (2 S ) π + π + π − decay is confirmed using the ψ (2 S ) → J/ψπ + π − decay mode. Ratios of the branching fractions of these four $$ {B}_c^{+} $$ <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> decay channels are measured.