  We consider non-chiral, full Lorentz group-based Plebanski formulation of
general relativity in its version that utilizes the Lagrange multiplier field
Phi with "internal" indices. The Hamiltonian analysis of this version of the
theory turns out to be simpler than in the previously considered in the
literature version with Phi carrying spacetime indices. We then extend the
Hamiltonian analysis to a more general class of theories whose action contains
scalars invariants constructed from Phi. Such theories have recently been
considered in the context of unification of gravity with other forces. We show
that these more general theories have six additional propagating degrees of
freedom as compared to general relativity, something that has not been
appreciated in the literature treating them as being not much different from
GR.
