Certain configurations of massive structures projected along the line of sight maximize the number of detections of gravitationally lensed $zsim10$ galaxies. We characterize such lines of sight with the etendue $sigma_mu$, the area in the source plane magnified over some threshold $mu$. We use the Millennium I and Millennium XXL cosmological simulations to determine the frequency of high $sigma_mu$ beams on the sky, their properties, and efficient selection criteria. We define the best beams as having $sigma_{mu>3} >2000$ arcsec$^2$, for a $zsim10$ source plane, and predict $477 pm 21$ such beams on the sky. The total mass in the beam and $sigma_{mu>3}$ are strongly correlated. After controlling for total mass, we find a significant residual correlation between $sigma_{mu>3}$ and the number of cluster-scale halos ($>10^{14} M_odot h^{-1}$) in the beam. Beams with $sigma_{mu>3} >2000$ arcsec$^2$, which should be best at lensing $zsim10$ galaxies, are ten times more likely to contain multiple cluster-scale halos than a single cluster-scale halo. Beams containing an Abell 1689-like massive cluster halo often have additional structures along the line of sight, including at least one additional cluster-scale ($M_{200}>10^{14}M_odot h^{-1}$) halo 28% of the time. Selecting beams with multiple, massive structures will lead to enhanced detection of the most distant and intrinsically faint galaxies.
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