We theoretically consider the possibility of using a few-mode fiber (FMF) and mode-division-multiplexing (MDM) to construct a quasi-distributed network of absorption-based fiber optical sensors. In this design, we utilize the low-attenuation fundamental linearly polarized (LP) mode for signal transmission, and a high-attenuation LP mode for absorption-based sensing. We develop a matrix formalism and use it to analyze the performance of such a MDM sensor network. We demonstrate that such a sensor network can indeed combine high sensitivity with large scale multiplexing, which is very difficult to achieve in traditional single-mode-fiber-based sensor networks.