The agile generation and control of multiple optical frequency modes combined with the realtime processing of multi-mode data provides access to experimentation in domains such as optomechanical systems, optical information processing, and multi-mode spectroscopy. The latter, specifically spectroscopy of spectral-hole burning (SHB), has motivated our development of a multi-mode heterodyne laser interferometric scheme centered around a software-defined radio platform for signal generation and processing, with development in an entirely open-source environment. A challenge to SHB is the high level of shot noise due to the laser power constraint imposed by the spectroscopic sample. Here, we have demonstrated the production, detection, and separation of multiple optical frequency modes to the benefit of optical environment sensing for realtime phase noise subtraction as well as shot noise reduction through multi-mode averaging. This has allowed us to achieve improved noise performance in low-optical-power interferometry. Although our target application is laser stabilization via SHB in cryogenic temperature rare-earth doped crystals, these techniques may be employed in a variety of different contexts.