We present new deep, wide-field imaging data from the Large Binocular Telescope (LBT) in g and r bands from the Smallest Scale of Hierarchy Survey (SSH) that reveal 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 1.2x10^7^M_{sun}_ to 1.4x10^8^M_{sun}_. The six dwarfs are located 1-2Mpc away from large galaxies, which implies that the observed distortions are unlikely to be due to tidal effects from a nearby, massive companion. At the distances of ~3-4Mpc at which the dwarfs lie, the identified tidal features are all resolved into individual stars in the LBT images and appear to consist of a population older than 1-2Gyr. This excludes 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 witness the hierarchical merging assembly of these dwarfs with their satellite populations. This scenario is also supported by the peculiar morphology and disturbed velocity field of their HI component. From the SSH sample, we estimate that a fraction of ~13% of the late-type dwarfs show signs of merging with satellites. This is in agreement with other recent independent studies and theoretical predictions within the {LAMNDA}CDM cosmological framework.