  We investigate the gravitational lensing properties of lines of sight
containing multiple cluster-scale halos, motivated by their ability to lens
very high-redshift (z ~ 10) sources into detectability. We control for the
total mass along the line of sight, isolating the effects of distributing the
mass among multiple halos and of varying the physical properties of the halos.
Our results show that multiple-halo lines of sight can increase the magnified
source-plane region compared to the single cluster lenses typically targeted
for lensing studies, and thus are generally better fields for detecting very
high-redshift sources. The configurations that result in optimal lensing cross
sections benefit from interactions between the lens potentials of the halos
when they overlap somewhat on the sky, creating regions of high magnification
in the source plane not present when the halos are considered individually. The
effect of these interactions on the lensing cross section can even be
comparable to changing the total mass of the lens from 10^15 M_sun to 3x10^15
M_sun. The gain in lensing cross section increases as the mass is split into
more halos, provided that the lens potentials are projected close enough to
interact with each other. A nonzero projected halo angular separation, equal
halo mass ratio, and high projected halo concentration are the best mass
configurations, whereas projected halo ellipticity, halo triaxiality, and the
relative orientations of the halos are less important. Such high mass,
multiple-halo lines of sight exist in the SDSS.
