  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 interactions between a single massless
tensor field with the mixed symmetry (3,1) and one massless tensor field with
the mixed symmetry (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 dual linearized gravity in D=6
gets coupled to a purely spin-two field with the mixed symmetry of the Riemann
tensor such that both the gauge transformations and first-order reducibility
relations in the (3,1) sector are changed, but not the gauge algebra.
