  Physical collisions between stars occur frequently in dense star clusters,
either via close encounters between two single stars, or during strong
dynamical interactions involving binary stars. Here we study stellar collisions
that occur during binary-single and binary-binary interactions, by performing
numerical scattering experiments. Our results include cross sections, branching
ratios, and sample distributions of parameters for various outcomes. For
interactions of hard binaries containing main-sequence stars, we find that the
normalized cross section for at least one collision to occur (between any two
of the four stars involved) is essentially unity, and that the probability of
collisions involving more than two stars is significant. Hydrodynamic
calculations have shown that the effective radius of a collision product can be
2-30 times larger than the normal main-sequence radius for a star of the same
total mass. We study the effect of this expansion, and find that it increases
the probability of further collisions considerably. We discuss these results in
the context of recent observations of blue stragglers in globular clusters with
masses exceeding twice the main-sequence turnoff mass. We also present Fewbody,
a new, freely available numerical toolkit for simulating small-N gravitational
dynamics that is particularly suited to performing scattering experiments.
