  In this paper we consider 3-form dark energy (DE) models with interactions in
the dark sector. We aim to distinguish the phenomenological interactions that
are defined through the dark matter (DM) and the DE energy densities. We do our
analysis mainly in two stages. In the first stage, we identify the
non-interacting 3-form DE model which generically leads to an abrupt late-time
cosmological event which is known as the little sibling of the Big Rip (LSBR).
We classify the interactions which can possibly avoid this late-time abrupt
event. We also study the parameter space of the model that is consistent with
the interaction between DM and DE energy densities at present as indicated by
recent studies based on BAO and SDSS data. In the later stage, we
observationally distinguish those interactions using the statefinder hierarchy
parameters $\{ S_{3}^{(1)}\,,\, S_{4}^{(1)}\} \,,\,\{ S_{3}^{(1)}\,,\,
S_{5}^{(1)}\} .$ We also compute the growth factor parameter $\epsilon(z)$ for
the various interactions we consider herein and use the composite null
diagnostic (CND) $\{ S_{3}^{(1)}\,,\,\epsilon(z)\} $ as a tool to characterise
those interactions by measuring their departures from the concordance model. In
addition, we make a preliminary analysis of our model in light of the recently
released data by SDSS~III on the measurement of the linear growth rate of
structure.
