  Motivated by a possible interplay between the mechanism of dynamical symmetry
breaking and the seesaw mechanism for generating fermion masses, we present a
scale-invariant model that extends the gauge symmetry of the Standard Model
electroweak sector to SU(3)$_L\otimes$U(1)$_X\otimes$U(1)$_N$, with a built-in
$B-L$ symmetry. The model is based on the symmetry structure of the known 3-3-1
models and, thus, it relates the number of the three observed fermion
generations with the cancellation of gauge anomalies. Symmetry breaking is
triggered via the Coleman-Weinberg mechanism taking into account a minimal set
of scalar field multiplets. We establish the stability conditions for the
tree-level scalar potential imposing the copositivity criteria and use the
method of Gildener-Weinberg for computing the one-loop effective potential when
one has multiple scalar fields. With the addition of vectorial fermions,
getting their mass mainly through the vacuum expectation value of scalar
singlets at $10^3$ TeV, the $B-L$ symmetry leads to textures for the fermion
mass matrices, allowing seesaw mechanisms for neutrinos and quarks to take
place. In particular, these mechanisms could partly explain the mass
hierarchies of the quarks. Once the breakdown of the SU(3)$_L$ symmetry is
supposed to occur around 10 TeV, the model also predicts new particles with
TeV-scale masses, such as a neutral scalar, $H_{1}$, a charged scalar, $H^\pm$,
and the gauge bosons $Z^{\prime}$, $W^{\prime\pm}$ and $Y^0$, that could be
searched with the high-luminosity LHC.
