  We discuss the role of Poisson-Nijenhuis geometry in the definition of
multiplicative integrable models on symplectic groupoids. These are integrable
models that are compatible with the groupoid structure in such a way that the
set of contour levels of the hamiltonians in involution inherits a topological
groupoid structure. We show that every maximal rank PN structure defines such a
model. We consider the examples defined on compact hermitian symmetric spaces
and studied in [arXiv:1503.07339].
