  A search for Higgs boson pair (HH) production in association with a vector
boson V (W or Z boson) is presented. The search is based on proton-proton
collision data at a center-of-mass energy of 13 TeV, collected with the CMS
detector at the LHC, corresponding to an integrated luminosity of 138
fb$^{-1}$. All hadronic and leptonic decays of V bosons are used. The leptons
considered are electrons, muons, and neutrinos. The HH production is searched
for in the $\mathrm{b\bar{b}b\bar{b}}$ decay channel. An observed (expected)
upper limit at 95% confidence level of VHH production cross section is set at
294 (124) times the standard model prediction. Constraints are also set on the
modifiers of the Higgs boson trilinear self-coupling, $\kappa_{\lambda}$,
assuming $\kappa_{2\mathrm{V}}$ = 1 and vice versa on the coupling of two Higgs
bosons with two vector bosons, $\kappa_{2\mathrm{V}}$. The observed (expected)
95% confidence intervals of these coupling modifiers are -37.7 $\lt$
$\kappa_{\lambda}$ $\lt$ 37.2 (-30.1 $\lt$ $\kappa_{\lambda}$ $\lt$ 8.9) and
-12.2 $\lt$ $\kappa_{2\mathrm{V}}$ $\lt$ 13.5 (-7.2 $\lt$
$\kappa_{2\mathrm{V}}$ $\lt$ 8.9), respectively.
