The Sun regularly releases considerable amounts of energy resulting in coronal mass ejections (CMEs) and accelerated particles, which can have a variety of adverse space weather (SW) effects at Earth and in the near-Earth environment. A useful means of tracking SW activity is via solar radio bursts (SRBs) associated with CMEs and solar energetic particle events (SEPs); CME-driven shocks can be tracked via Type II SRBs, while energetic electrons escaping into the heliosphere can be tracked via Type III SRBs. Currently, there are no operational means to monitor and track SRBs throughout the inner heliosphere. Here, we propose a constellation of CubeSats called SURROUND to observe SRBs in order to track CME and SEPs for SW monitoring. This concept would complement the mission goals of ESA Solar Orbiter/RPW, NASA Parker Solar Probe/FIELDS and SunRISE, among other missions.