  The consistent interactions between a single, free, massless tensor gauge
field with the mixed symmetry $(3,1)$ and an Abelian $p$-form are investigated
in the framework of the BRST formalism combined with cohomological techniques.
Under the assumptions on smoothness, locality, Lorentz covariance, and
Poincar\'{e} invariance of the deformations, supplemented by the requirement
that the interacting Lagrangian is at most second-order derivative, it is
proved that for every value $p\geq 1$ of the form degree there are consistent
couplings between the Abelian form and the massless $(3,1)$ gauge field.
