  Under the general hypotheses of locality, smoothness of interactions in the
coupling constant, Poincare invariance, Lorentz covariance, and preservation of
the number of derivatives on each field, we investigate the cross-couplings of
one or several spin-two fields to a massless p-form. Two complementary cases
arise. The first case is related to the standard interactions from General
Relativity, but the second case describes a new, special type of couplings in
D=p+2 spacetime dimensions, which break the PT-invariance. Nevertheless, no
consistent, indirect cross-interactions among different gravitons with a
positively defined metric in internal space can be constructed.
