Robust systems, like the molecular networks of living cells, are often resistant to single hits such as those caused by high-specificity drugs. Here we show that partial weakening of the Escherichia coli and Saccharomyces cerevisiae transcriptional regulatory networks at a small number (3-5) of selected nodes can have a greater impact than the complete elimination of a single selected node. In both cases, the targeted nodes have the greatest possible impact; still, the results suggest that in some cases broader specificity compounds or multitarget drug therapies may be more effective than individual high-affinity, high-specificity ones. Multiple but partial attacks mimic well a number of in vivo scenarios and may be useful in the efficient modification of other complex systems.