  We investigate the influence of self-energy diagrams beyond the two-particle
vertex level within dual fermion theory. Specifically, we calculate the local
three-particle vertex and construct from it selected dual fermion self-energy
corrections to dynamical mean field theory. For the two-dimensional Hubbard
model, the thus obtained self-energy corrections are small in the parameter
space where dual fermion corrections based on the two-particle vertex only are
small. However, in other parts of the parameter space, they are of a similar
magnitude and qualitatively different from standard dual fermion theory. The
high-frequency behaviour of the self-energy correction is - surprisingly - even
dominated by corrections stemming from the three-particle vertex.
