The $Upsilon(1S)mu^+mu^-$ invariant-mass distribution is investigated for a possible exotic meson state composed of two $b$ quarks and two $overline{b}$ quarks, $X_{boverline{b}boverline{b}}$. The analysis is based on a data sample of $pp$ collisions recorded with the LHCb detector at centre-of-mass energies $sqrt{s} =$ 7, 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 $X_{boverline{b}boverline{b}}$ state. The limits are set in the fiducial volume where all muons have pseudorapidity in the range $[2.0,5.0]$, and the $X_{boverline{b}boverline{b}}$ state has rapidity in the range $[2.0,4.5]$ and transverse momentum less than 15 GeV/$c$.
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