A special version of multi-reference perturbation theory is investigated which differs from standard ones by using a zeroth order Hamiltonian that contains two-electron terms explicitly. The method is applicable to reference states that can be written as an antisymmetrized product of two or more electron functions. In that case the zeroth order Hamiltonian has a well defined physical meaning and the matrix elements that come about can be evaluated in an efficient manner. We implemented the theory for the antisymmetrized product of strongly orthogonal geminals wave function and, as a special case, for the generalized valence bond. Illustrative calculations on sample molecules show the reliability of the approach, as well as a significant improvement in many cases compared to MRPT versions based on one-body zeroth order Hamiltonians.