  Over the last few decades, observational surveys have revealed that
high-order multiple-star systems (e.g. triples, quadruples, etc.), and triples
in particular, are common in our Galaxy. In this paper, we consider the
dynamical significance of this transformation in our understanding of stellar
multiplicity. Using empirically constrained binary and triple fractions in
those star clusters for which these values are available in the literature, we
compare analytic rates for encounters involving single, binary, and triple
stars. Our results show that, \textit{even for relatively low triple fractions,
dynamical interactions involving triples occur roughly as often as encounters
involving either single or binary stars alone, particularly in low-mass star
clusters}. More generally, using empirically-derived multiple star catalogues
for the young star-forming association Taurus-Auriga and the Galactic field, we
show that the data are consistent with the gravitationally-focused cross
section for encounters increasing with increasing multiplicity. Consequently,
triple stars, and even higher-order multiples, could be more important than
previously realized for a number of astrophysical phenomena, including the
formation and destruction of compact binaries and various types of stellar
exotica, and the dynamical evolution of star clusters.
