Microlensing is increasingly gaining recognition as a powerful method for t
he detection and characterization of extrasolar planetary systems. Naively,
one might expect that the probability of detecting the influence of more t
han one planet on any single microlensing light curve would be small. Recen
tly, however, Griest & Safizadeh have shown that, for a subset of events, t
hose with minimum-impact parameter u(min) less than or similar to 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 primar
y Einstein ring radius R-E and remains substantial outside this zone. In th
is Letter, we point out that this result implies that, regardless of orient
ation, all Jovian-mass planets with separations near 0.6-1.6R(E) dramatical
ly affect the central region of the magnification pattern and thus have a s
ignificant probability of being detected (or ruled out) in high-magnificati
on events. The joint probability, averaged over all inclinations and phases
, of two planets having projected separations within 0.6-1.6R(E) is substan
tial: 1%-15% for two planets with the intrinsic separations of Jupiter and
Saturn orbiting around 0.3-1.0 M. parent stars. We illustrate by example th
e complicated magnification patterns and light curves that can result when
two planets are present, and we discuss the possible implications of our re
sult on detection efficiencies and the ability to discriminate between mult
iple and single planets in high-magnification events.