  Gaudi & Gould (1997) showed that close companions of remote binary systems
can be efficiently detected by using gravitational microlensing via the
deviations in the lensing light curves induced by the existence of the lens
companions. In this paper, we introduce another channel to detect faint
close-in binary companions by using microlensing. This method utilizes a
caustic-crossing binary lens event with a source also composed of binary stars,
where the companion is a faint star. Detection of the companion is possible
because the flux of the companion can be highly amplified when it crosses the
lens caustic. The detection is facilitated since the companion is more
amplified than the primary because it, in general, has a smaller size than the
primary, and thus experiences less finite source effect. The method is
extension of the previous one suggested to detect close-in giant planets by
Graff & Gaudi (2000) and Lewis & Ibata (2000) and further developed by Ashton &
Lewis (2001). From the simulations of realistic Galactic bulge events, we find
that companions of K-type main sequence or brighter can be efficiently detected
from the current type microlensing followup observations by using the proposed
method. We also find that compared to the method of detecting lens companions
for which the efficiency drops significantly for binaries with separations
$\lesssim 0.2$ of the angular Einstein ring radius, the proposed method has an
important advantage of being able to detect companions with substantially
smaller separations down to order of 0.01 \theta_E.
