The striatum comprises a network characterized by a highly shared feedforward inhibition (FFI) mediated by fast-spiking interneurons (FSI), which constitute only 1% of the striatal population. We investigated the dynamical consequences of this extensively shared FFI beyond inducing synchrony in a local striatal microcircuit. Our findings reveal that increased FFI sharing enhances the across-trial variability of striatal responses, activity of medium spiny neurons (MSNs), to cortical inputs, and endows the striatal network with the capacity to modulate output correlations in a bidirectional manner. Specifically, weakly shared cortical inputs become more correlated, whereas strongly shared cortical inputs are decorrelated in the presence of FSIs. These dynamic modulatory effects on MSNs, in turn, substantially alter the spiking statistics of downstream neurons in the globus pallidus, regarding across-trial variability and burstiness.