  A search for the production of events containing three W bosons predicted by
the standard model is reported. The search is based on a data sample of
proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the
CMS experiment at the CERN LHC and corresponding to a total integrated
luminosity of 35.9 fb$^{-1}$. The search is performed in final states with
three leptons (electrons or muons), or with two same-charge leptons plus two
jets. The observed (expected) significance of the signal for
W$^\pm$W$^\pm$W$^\mp$ production is 0.60 (1.78) standard deviations, and the
ratio of the measured signal yield to that expected from the standard model is
0.34 $^{+0.62}_{-0.34}$. Limits are placed on three anomalous quartic gauge
couplings and on the production of massive axionlike particles.
