TESS will conduct a two-year survey for transiting planets over 90% of the sky. Once this survey is complete, in late 2019, what should the spacecraft do next? There do not appear to be any fundamental obstacles to continued operation for another 5-10 years. We are investigating plans for a TESS Extended Mission, by conducting trade studies of different scenarios for continuing the planet search for an additional few years.
Building on previous work  we perform Monte Carlo simulations of the population of TESS planet detections for several plausible sky-scanning strategies: repeating the all-sky survey, concentrating on the ecliptic poles, or concentrating on the ecliptic plane. For a one-year extended mission, we find that the ecliptic-pole strategy maximizes the number of newly detected planets with relatively long orbital periods (P > 20d), planets within the habitable zone, and multiple-planet systems. Observations focused on the ecliptic plane would provide nearly the same total number of new planets (~700), but they would orbit brighter host stars, making them more amenable to atmospheric characterization. These and related predictions will inform mission planning, and in the longer term will assist the community in preparing radial velocity and transit follow-up programs.
 Sullivan, Winn, Berta-Thompson et al. 2015. ApJ. http://arxiv.org/pdf/1506.03845v2.pdf.