We describe the development of a cryogenic multiplexer for far-infrared (FIR) photoconductor detectors operating at moderate backgrounds. The device is called the SBRC 190. Its architecture and basic functions are based on the 1×32-channel CRC 696 CMOS device used on SIRTF. The SBRC 190 is designed to accommodate the higher backgrounds to be encountered on SOFIA and Herschel, to tolerates a wider range of backgrounds, to permit faster sampling, and to facilitate synchronization of sampling with chopping. Major design differences relative to the CRC 696 which have been incorporated in the SBRC 190 design are: (a) an AC coupled, capacitive feedback transimpedence unit cell, which minimizes input offset effects, thereby enabling low detector biases, (b) selectable feedback capacitors to enable operation over a wide range of backgrounds, and (c) clamp and sample-and-hold output circuits to improve sampling efficiency, which can be a concern at the relatively high readout rates required. A relationship between sampling efficiency and noise performance needed to achieve background-limited instrument performance (BLIP) is derived. Requirements for use on SOFIA, the basic circuit design, fabrication, and operation are discussed.