  The Transiting Exoplanet Survey Satellite (TESS) will perform a two-year
survey of nearly the entire sky, with the main goal of detecting exoplanets
smaller than Neptune around bright and nearby stars. There do not appear to be
any fundamental obstacles to continuing science operations for at least several
years after the two-year Primary Mission. To provide a head start to those who
will plan and propose for such a mission, we present simulations of exoplanet
detections in a third year of TESS operations. Our goal is to provide a helpful
reference for the exoplanet-related aspects of any Extended Mission, while
recognizing this will be only one part of a larger community discussion of the
scientific goals. We use Monte Carlo simulations to try and anticipate the
quantities and types of planets that would be detected in each of 6 plausible
scenarios for a one-year Extended Mission following the two-year Primary
Mission. We find that: (1) there is no sharp fall-off in the planet discovery
rate in the third year; (2) the quantity of newly detected sub-Neptune radius
planets does not depend strongly on the schedule of pointings; (3) an important
function of an Extended Mission would be improving our ability to predict the
times of future transits and occultations of TESS-detected planets.
