  We solve the problem of constructing consistent first-order
cross-interactions between spin-2 and spin-3 massless fields in flat spacetime
of arbitrary dimension n > 3 and in such a way that the deformed gauge algebra
is non-Abelian. No assumptions are made on the number of derivatives involved
in the Lagrangian, except that it should be finite. Together with locality, we
also impose manifest Poincare invariance, parity invariance and analyticity of
the deformations in the coupling constants.
