Microlensing is increasingly gaining recognition as a powerful method for the detection and characterization of extra-solar planetary systems . Naively , one might expect that the probability of detecting the influence of more than one planet on any single microlensing light curve would be small . Recently , however , Griest & Safizadeh ( 1998 ) have shown that , for a subset of events , those with minimum impact parameter u _ { min } { { } _ { < } \atop { } ^ { { } ^ { \sim } } } 0.1 ( high magnification events ) , the detection probability is nearly 100 % for Jovian mass planets with projected separations in the range 0.6–1.6 of the primary Einstein ring radius R _ { E } , and remains substantial outside this zone . In this Letter , we point out that this result implies that , regardless of orientation , all Jovian mass planets with separations near 0.6–1.6 R _ { E } dramatically affect the central region of the magnification pattern , and thus have a significant probability of being detected ( or ruled out ) in high magnification events . The probability , averaged over all orbital phases and inclination angles , of two planets having projected separations within 0.6 – 1.6 R _ { E } is substantial : 1-15 % for two planets with the intrinsic orbital separations of Jupiter and Saturn orbiting around 0.3–1.0 M _ { \odot } parent stars . We illustrate by example the complicated magnification patterns and light curves that can result when two planets are present , and discuss possible implications of our result on detection efficiencies and the ability to discriminate between multiple and single planets in high magnification events .