  The short-range part of the neutrinoless double beta amplitude is generated
via the exchange of exotic particles, such as charged scalars, leptoquarks
and/or diquarks. In order to give a sizeable contribution to the total decay
rate, the masses of these exotics should be of the order of (at most) a few
TeV. Here, we argue that these exotics could be the "light" (i.e weak-scale)
remnants of some $B-L$ violating variants of $SU(5)$. We show that unification
of the standard model gauge couplings, consistent with proton decay limits, can
be achieved in such a setup without the need to introduce supersymmetry. Since
these non-minimal $SU(5)$-inspired models violate $B-L$, they generate Majorana
neutrino masses and therefore make it possible to explain neutrino oscillation
data. The "light" coloured particles of these models can potentially be
observed at the LHC, and it might be possible to probe the origin of the
neutrino masses with $\Delta L=2$ violating signals. As particular realizations
of this idea, we present two models, one for each of the two possible
tree-level topologies of neutrinoless double beta decay.
