  Consider a finite system of competing Brownian particles on the real line.
Each particle moves as a Brownian motion, with drift and diffusion coefficients
depending only on its current rank relative to the other particles. We find a
sufficient condition for a.s. absence of a total collision (when all particles
collide) and of other types of collisions, say of the three lowest-ranked
particles. This continues the work of Ichiba, Karatzas, Shkolnikov (2013) and
Sarantsev (2015).
