  We consider the dynamics of a reaction-diffusion system on a multigraph. The
species share the same set of nodes but can access different links to explore
the embedding spatial support. By acting on the topology of the networks we can
control the ability of the system to self-organise in macroscopic patterns,
emerging as a symmetry breaking instability of an homogeneous fixed point. Two
different cases study are considered: on the one side, we produce a global
modification of the networks, starting from the limiting setting where species
are hosted on the same graph. On the other, we consider the effect of inserting
just one additional single link to differentiate the two graphs. In both cases,
patterns can be generated or destroyed, as follows the imposed, small,
topological perturbation. Approximate analytical formulae allows to grasp the
essence of the phenomenon and can potentially inspire innovative control
strategies to shape the macroscopic dynamics on multigraph networks
