  On the basis of recent results extending non-trivially the Poincar\'e
symmetry, we investigate the properties of bosonic multiplets including
$2-$form gauge fields. Invariant free Lagrangians are explicitly built which
involve possibly $3-$ and $4-$form fields. We also study in detail the
interplay between this symmetry and a U(1) gauge symmetry, and in particular
the implications of the automatic gauge-fixing of the latter associated to a
residual gauge invariance, as well as the absence of self-interaction terms.
