What is a good number of people to network with at each firm?

So I've generally heard that you should network/meet as many people as possible but the responses in this post make me a little weary to consider what had seemed like conventional wisdom. Assuming that each call goes well, what is the right number of people to call from each firm? Taking it even further is there a number of people that you should speak to depending on their position (i.e. 2 analysts, 1 associate).

I'm avoiding being too pushy (e.g. only emailing one person at a time, sending just one follow up email per person) but have still been able to have a good amount of calls so far.