The number of waveguide tapsNthat a passive optical fiber bus can accommodate is typically quite low, due to significant attenuation of the signal in the taps and splices. In an effort to increaseNsubstantially, this paper investigates the potential use of optical amplifiers to boost the signal along the bus. An analysis is performed for both direct detection and heterodyne detection. Values ofNare determined for a wide range of system and device parameters, such as signal duration, amplifier noise bandwidth, and amplifier saturation power. It is found that the use of optical amplifiers can increaseNby at least an order of magnitude, and by as much as two orders of magnitude under many circumstances.