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Constraint on Additional Planets in Planetary Systems Discovered through the Channel of High-magnification Gravitational Microlensing Events

High-magnification gravitational microlensing events provide an important channel of detecting planetary systems with multiple giants located at their birth places. In order to investigate the potential existence of additional planets, we reanalyze the light curves of the eight high-magnification microlensing events for each of which a single planet was previously detected. The analyzed events include OGLE-2005-BLG-071, OGLE-2005-BLG-169, MOA-2007-BLG-400, MOA-2008-BLG-310, MOA-2009-BLG-319, MOA-2009-BLG-387, MOA-2010-BLG-477, and MOA-2011-BLG-293. We find that including an additional planet improves fits with $Δχ^2 < 80$ for seven out of eight analyzed events. For MOA-2009-BLG-319, the improvement is relatively big with $Δχ^2 \sim 143$. From inspection of the fits, we find that the improvement of the fits is attributed to systematics in data. Although no clear evidence of additional planets is found, it is still possible to constrain the existence of additional planets in the parameter space. For this purpose, we construct exclusion diagrams showing the confidence levels excluding the existence of an additional planet as a function of its separation and mass ratio. We also present the exclusion ranges of additional planets with 90\% confidence level for Jupiter, Saturn, and Uranus-mass planets.