  We present new deep, wide-field Large Binocular Telescope (LBT) $g$ and $r$
imaging data from the Smallest Scale of Hierarchy Survey (SSH) revealing
previously undetected tidal features and stellar streams in the outskirts of
six dwarf irregular galaxies (NGC 5238, UGC 6456, UGC 6541, UGC 7605, UGC 8638,
and UGC 8760) with stellar masses in the range $1.2 \times 10^7$ M$_{\odot}$ to
$1.4 \times 10^8$ M$_{\odot}$. The six dwarfs are located 1-2 Mpc away from
large galaxies, implying that the observed distortions are unlikely to be due
to tidal effects from a nearby, massive companion. At the dwarfs' distances of
$\sim$3-4 Mpc, the identified tidal features are all resolved into individual
stars in the LBT images and appear to be made of a population older than 1-2
Gyr, excluding the possibility that they result from irregular and asymmetric
star formation episodes that are common in gas-rich dwarf galaxies. The most
plausible explanation is that we are witnessing the hierarchical merging
assembling of these dwarfs with their satellite populations, a scenario also
supported by the peculiar morphology and disturbed velocity field of their HI
component. From the SSH sample we estimate a fraction of late type dwarfs
showing signs of merging with satellites of $\sim$13\%, in agreement with other
recent independent studies and theoretical predictions within the $\Lambda$CDM
cosmological framework.
