  We present the results of a long-term periodicity search in a sample of
$\gamma$-ray blazars within a multiwavelength context. These blazars have been
selected from the Steward Observatory sample as part of its optical monitoring
program between 2008 and 2018. We study 15 sources with a temporal coverage in
their optical total and polarized emission sufficiently large ($>9$ years) to
perform a reliable long-term periodicity analysis. We collect data from several
observatories to extend the coverage, enabling the search of longer periods. In
addition, data are also gathered in the high-energy ($E>100$ MeV) $\gamma$-ray
band from the $\textit{Fermi}$ Large Area Telescope; and in the 15-GHz radio
band from the Owens Valley Radio Observatory. We identify 5 promising
candidates to host quasi-periodic emission, AO 0235+164, PKS 1222+216, Mrk 501,
BL Lacertae and 1ES 2344+514 with periods in one or more bands and statistical
significances $\sim$3$\sigma$ after trial factor correction. AO 0235+164 shows
a period of $\sim$8.2 years in the R band; PKS 1222+216 has a quasi-periodic
modulation in its total and polarized optical emission of $\sim$1.6 years; Mrk
501 displays a $\sim$5-year quasi-periodicity in optical and radio wavelengths;
BL Lacertae presents a period of $\sim$1.8 years in its polarized emission; and
1ES 2344+514 shows a hint of a $\sim$5.5-year period in its optical R band. We
interpret these results in the framework of the most common models and
scenarios, namely the presence of a binary supermassive black hole system; or
geometrical effects like helical or precessing jets.
