Unless you're hiring for rare roles that require niche skills, it's unlikely that you'll get people that are in overlapping networks. If you do, you might be encountering the problem where Company A has a bunch of people that used to work at Company B. Now Company A is just an "old boys club" from Company B and is biased towards their old colleagues.

If you ask for single referrals, how do you combat the problem of people just recommended people based on friendships and not actually work quality?