  Under the hypotheses of analyticity, locality, Lorentz covariance, and
Poincare invariance of the deformations, combined with the requirement that the
interaction vertices contain at most two spatiotemporal derivatives of the
fields, we investigate the consistent selfinteractions that can be added to a
collection of massless tensor fields with the mixed symmetry (3,1) and
respectively (2,2). The computations are done with the help of the deformation
theory based on a cohomological approach, in the context of the antifield-BRST
formalism. Our result is that no selfinteractions that deform the original
gauge transformations emerge. In the case of the collection of (2,2) tensor
fields it is possible to add a sum of cosmological terms to the free
Lagrangian.
