  Non-trivial, consistent interactions of a free, massless tensor field t_{\mu
\nu |\alpha \beta} with the mixed symmetry of the Riemann tensor are studied in
the following cases: self-couplings, cross-interactions with a Pauli-Fierz
field and cross-couplings with purely matter theories. The main results,
obtained from BRST cohomological techniques under the assumptions on
smoothness, locality, Lorentz covariance and Poincar\'{e} invariance of the
deformations, combined with the requirement that the interacting Lagrangian is
at most second-order derivative, can be synthesized into: no consistent
self-couplings exist, but a cosmological-like term; no cross-interactions with
the Pauli-Fierz field can be added; no non-trivial consistent cross-couplings
with the matter theories such that the matter fields gain gauge transformations
are allowed.
