We show that KMT-2016-BLG-1107 displays a new type of degeneracy between wide-binary and close-binary Hollywood events in which a giant-star source envelops the planetary caustic. The planetary anomaly takes the form of a smooth, two-day "bump" far out on the falling wing of the light curve, which can be interpreted either as the source completely enveloping a minor-image caustic due to a close companion with mass ratio q=0.036, or partially enveloping a major-image caustic due to a wide companion with q=0.004. The best estimates of the companion masses are both in the planetary regime (3.3−1.8+3.5Mjup and 0.090−0.037+0.096Mjup) but differ by an even larger factor than the mass ratios due to different inferred host masses. We show that the two solutions can be distinguished by high-resolution imaging at first light on next-generation ("30m") telescopes. We provide analytic guidance to understand the conditions under which this new type of degeneracy can appear.