Mixed Reality (MR) is becoming ubiquitous as it finds its applications in education, healthcare, and other sectors beyond leisure. While MR end devices, such as headsets, have low energy intensity, the total number of devices and resource requirements of the entire MR ecosystem, which includes cloud and edge endpoints, can be significant. The resulting operational and embodied carbon footprint of MR has led to concerns about its environmental implications. Recent research has explored reducing the carbon footprint of MR devices by exploring hardware design space or network optimizations. However, many additional avenues for enhancing MR's sustainability remain open, including energy savings in non-processor components and carbon-aware optimizations in collaborative MR ecosystems. In this paper, we aim to identify key challenges, existing solutions, and promising research directions for improving MR sustainability. We explore adjacent fields of embedded and mobile computing systems for insights and outline MR-specific problems requiring new solutions. We identify the challenges that must be tackled to enable researchers, developers, and users to avail themselves of these opportunities in collaborative MR systems.