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?
> it's unlikely that you'll get people that are in overlapping networks
Networks all overlap if you search deep enough, ask Kevin Bacon. For good-enough talent and starting with random nodes, yeah, you'll probably not overlap. But there's a few dozen people of top talent for any particular role you're looking for, so by the time you iterate to the top of the tree, you really do get a lot of repeats.