After posting, I realized that there may have been a number of third-body satellite captures in the asteroid belt, but they did not result in an increase in the number of satellites.
Let’s say you already have two asteroids in orbit about each other, call them A (larger) and B (smaller). Object C makes a close approach. If it happens to hit the right spot, it could exchange velocity with object B so that C goes into orbit around A. But then B will have more velocity, most likely enough that it leaves orbit. It’s also possible that B and C will end up in orbit about each other but not around A. In either case, the net change in the number of satellites is zero.