We show that the dynamical multistability of a network of bursting subthalamic neurons, caused by synaptic plasticity has a strong impact on the stimulus-response properties when exposed to weak and short desynchronizing stimuli. Intriguingly, such stimuli can reliably shift the network from a stable state with pathological synchrony and connectivity to a stable desynchronized state with down-regulated connectivity. However, unlike in the case of stronger coordinated reset stimulation, after termination of weaker stimulation the network may undergo a transient rebound of synchrony. When the coordinated reset stimulation is even weaker and/or shorter, so that a single stimulation epoch is not effective, the network dynamics and connectivity can still be reshaped in a cumulative manner by repetitive stimulation delivery.