  We conducted a survey of nearby binary systems composed of main sequence
stars of spectral types F and G in order to improve our understanding of the
hierarchical nature of multiple star systems. Using Robo-AO, the first robotic
adaptive optics instrument, we collected high angular resolution images with
deep and well-defined detection limits in the SDSS $i'$ band. A total of 695
components belonging to 595 systems were observed. We prioritized observations
of faint secondary components with separations over $10''$ to quantify the
still poorly constrained frequency of their sub-systems. Of the 214 secondaries
observed, 39 contain such subsystems; 19 of those were discovered with Robo-AO.
The selection-corrected frequency of secondary sub-systems with periods from
$10^{3.5}$ to $10^5$ days is 0.12$\pm$0.03, the same as the frequency of such
companions to the primary. Half of the secondary pairs belong to quadruple
systems where the primary is also a close pair, showing that the presence of
sub-systems in both components of the outer binary is correlated. The
relatively large abundance of 2+2 quadruple systems is a new finding, and will
require more exploration of the formation mechanism of multiple star systems.
We also targeted close binaries with periods less than 100~yr, searching for
their distant tertiary components, and discovered 17 certain and 2 potential
new triples. In a sub-sample of 241 close binaries, 71 have additional outer
companions. The overall frequency of tertiary components is not enhanced,
compared to all (non-binary) targets, but in the range of outer periods from
$10^6$ to $10^{7.5}$ days (separations on the order of 500~AU), the frequency
of tertiary components is 0.16$\pm$0.03, exceeding by almost a factor of two
the frequency of similar systems among all targets (0.09).
