We present results from composite plasmonic nanostructures designed to achieve the cascaded enhancement of electromagnetic fields at optical frequencies. Our structures comprise a small metallic nanodisc suspended above a larger disk. We probe the optical properties of these structures by coating them with a layer of a visible-light fluorophore and observing fluorescence signals with the help of scanning confocal microscopy. A 43 +/- 5-fold increase in the far-field fluorescence signal has been observed for two-tier composite nanostructures, when compared to the signal obtained from individual nanodiscs. Our results offer the prospect of using such nanostructures for field concentration, optical manipulation of nanoobjects, chemical and biological sensing.