  We present high sensitivity ($\sigma_P \simeq 0.6\,$mJy) polarimetric
observations in seven bands, from $2.1$ to $38\,$GHz, of a complete sample of
$104$ compact extragalactic radio sources brighter than $200\,$mJy at
$20\,$GHz. Polarization measurements in six bands, in the range $5.5-38\,$GHz,
for $53$ of these objects were reported by \citet{Galluzzi2017}. We have added
new measurements in the same six bands for another 51 sources and measurements
at $2.1\,$GHz for the full sample of $104$ sources. Also, the previous
measurements at $18$, $24$, $33$ and $38\,$GHz were re-calibrated using the
updated model for the flux density absolute calibrator, PKS1934-638, not
available for the earlier analysis. The observations, carried out with the
Australia Telescope Compact Array (ATCA), achieved a $90\%$ detection rate (at
$5\sigma$) in polarization. $89$ of our sources have a counterpart in the $72$
to $231\,$MHz GLEAM survey \citep{HurleyWalker2017}, providing an unparalleled
spectral coverage of $2.7$ decades of frequency for these sources. While the
total intensity data from $5.5$ to $38\,$GHz could be interpreted in terms of
single component emission, a joint analysis of more extended total intensity
spectra presented here, and of the polarization spectra, reveals that over
$90\%$ of our sources show clear indications of at least two emission
components. We interpret this as an evidence of recurrent activity. Our high
sensitivity polarimetry has allowed a $5\,\sigma$ detection of the weak
circular polarization for $\sim 38\%$ of the dataset, and a deeper estimate of
$20\,$GHz polarization source counts than has been possible so far.
