Find third and n-th level domains in a network

In this page an example about how domain naming works is provided.

The second-level domain is utexas.edu, then some third and fourth level domains are listed, like computerstore.utexas.edu and www.mccombs.utexas.edu.

Suppose that an entire network is coected to the inteet, and each of his hosts have a public IP. Is it possible, given a certain n-level domain belonging to that network, to know all the (n-1)-level subdomains? I mean: is it possible to list them through publicly available informations (DNS queries...)?

For example, given site.com, I would like to know if it is possible to know all its third-level associated domains (like www.site.com), given that they belong to the same owner and that they all have a public address.