  Consistent Hamiltonian interactions that can be added to an abelian free
BF-type class of theories in any n greater or equal to 4 spacetime dimensions
are constructed in the framework of the Hamiltonian BRST deformation based on
cohomological techniques. The resulting model is an interacting field theory in
higher dimensions with an open algebra of on-shell reducible first-class
constraints. We argue that the Hamiltonian couplings are related to a natural
structure of Poisson manifold on the target space.
