We continue with the construction of Poisson groupoid structures on moduli spaces of flat G-bundles over decorated surfaces. In this talk we consider a Lie 2-group structure on G which is compatible with an Ad-invariant metric on its Lie 2-algebra. By assuming the existence of such a Lie 2-group structure and a suitable Z_2-symmetry on the underlying decorated surface, we can construct up to three compatible Poisson groupoid structures on the associated moduli spaces which can be exemplified by considering Poisson 2-groups and some closely related symplectic groupoids.