  Statistics of hierarchical systems containing three or more stars are
continuously improving. The Multiple Star Catalog (MSC) is currently the most
comprehensive catalogue of multiple-star systems and contains component masses,
orbital periods, and additional information. The systems in the MSC are
interesting for several reasons, including the long-term dynamical evolution of
few-body systems. Although the secular evolution of triples and quadruples has
been explored before, a systematic study of the systems in the MSC including
also quintuples and sextuples has not been carried out. Here, we explore the
main-sequence (MS) evolution of stars from the MSC based on approximately
2x10^5 secular dynamical integrations. We estimate statistical probabilities
for strong interactions during the MS such as tidal evolution and mass
transfer, and the onset of dynamical instability. Depending on the assumed
model for the unknown orbital elements, we find that the fraction of
noninteracting systems is largest for triples (~0.9), and decreases to ~0.6-0.8
for sextuples. The fraction of strong interactions increases from ~0.1 to ~0.2
from triples to sextuples, and the fraction of dynamically unstable systems
increases from ~0.001 to ~0.1-0.2. The larger fractions of strong interactions
and dynamical instability in systems with increasing multiplicity can be
attributed to increasingly complex secular evolution in these systems. Our
results indicate that a significant fraction of high-multiplicity systems
interact or become dynamically unstable already during the MS, with an
increasing importance as the number of stars increases.
