  To date, in almost all strong gravitational lensing analyses for modeling
giant arc systems and multiple quasar images, it has been assumed that all the
deflecting matter is concentrated in one lens plane at a certain distance - the
thin lens approximation. However, in a few observed cases, lenses at more than
one redshift have been identified as contributing to the image splitting.
  Here we report on a quantitative investigation of the importance and
frequency of significant multiple lensing agents. We use multi-lens plane
simulations to evaluate how frequently two or more lens planes combined are
essential for multiple imaging, as compared with the cases where a single lens
plane alone provides enough focusing to be supercritical.
  We find that the fraction of cases for which more than one lens plane
contributes significantly to a multi-image lensing situation is a strong
function of source redshift. For sources at redshift unity, 95% of lenses
involve only a single mass concentration, but for a more typical scenario with,
e.g., a source at a redshift of z_s = 3.8, as many as 38% of the strongly
lensed quasars/arcs occur because of a significant matter contribution from one
or more ADDITIONAL lens planes. In the 30% to 40% of cases when additional
planes make a significant contribution, the surface mass density of the primary
lens will be overestimated by about 15% to 20%, if the additional contributions
are not recognized.
