  The upcoming TESS mission is expected to find thousands of transiting planets
around bright stars, yet for three-quarters of the fields observed the temporal
coverage will limit discoveries to planets with orbital periods below 13.7
days. From the Kepler catalog, the mean probability of these short-period
transiting planets having additional longer period transiters (which would be
missed by TESS) is 18%, a value ten times higher than the average star. In this
work, we show how this probability is not uniform but functionally dependent
upon the properties of the observed short-period transiters, ranging from less
than 1% up to over 50%. Using artificial neural networks (ANNs) trained on the
Kepler catalog and making careful feature selection to account for the
differing sensitivity of TESS, we are able to predict the most likely
short-period transiters to be accompanied by additional transiters. Through
cross-validation, we predict that a targeted, optimized TESS transit and/or
radial velocity follow-up program using our trained ANN would have a discovery
yield improved by a factor of two. Our work enables a near-optimal follow-up
strategy for surveys following TESS targets for additional planets, improving
the science yield derived from TESS and particularly beneficial in the search
for habitable-zone transiting worlds.
