A single biconical fiber taper is a simple and low-cost yet powerful sensor. With a distinct strength in refractive index (RI) sensing, biconical tapered fiber sensors can find their place in handheld sensor platforms, especially as biosensors that are greatly needed in health care, environmental protection, food safety, and biodefense. We report doubling of sensitivity for these sensors with two passes through the tapered region, which becomes possible through the use of sensitive and high-dynamic-range photodetectors. In a proof-of-principle experiment, we measured transmission through the taper when it was immersed in isopropyl alcohol-water mixtures of varying concentrations, in which a thin gold layer at the tip of the fiber acted as a mirror enabling two passes through the tapered region. This improved the sensitivity from 0.43 dB/vol % in the single-pass case to 0.78 dB/vol % with two passes through the taper. The refractive index detection limit was estimated to be ~1.2×10-5 RI units (RIU) and ~0.6×10-5 RIU in the single- and double-pass schemes, respectively. We predict that further enhancement of sensitivity may be achieved with a higher number of passes through the taper.