A bstract The ϒ (1 S ) μ + μ − invariant-mass distribution is investigated for a possible exotic meson state composed of two b quarks and two $$ \overline{b} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> quarks, $$ {X}_{b\overline{b}b\overline{b}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:msub> </mml:math> . The analysis is based on a data sample of pp collisions recorded with the LHCb detector at centre-of-mass energies $$ \sqrt{s}=7 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>7</mml:mn> </mml:math> , 8 and 13 TeV, corresponding to an integrated luminosity of 6.3 fb −1 . No significant excess is found, and upper limits are set on the product of the production cross-section and the branching fraction as functions of the mass of the $$ {X}_{b\overline{b}b\overline{b}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:msub> </mml:math> state. The limits are set in the fiducial volume where all muons have pseudorapidity in the range [2 . 0 , 5 . 0], and the $$ {X}_{b\overline{b}b\overline{b}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>X</mml:mi> <mml:mrow> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>b</mml:mi> <mml:mover> <mml:mi>b</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:msub> </mml:math> state has rapidity in the range [2 . 0 , 4 . 5] and transverse momentum less than 15 GeV/ c .