Two Nodes on Clearnet on Same Network?

Is it possible to run two nodes on the same network on Clearnet?

If not, why not? Do I have to essentially opt to run one on clearnet and not the other?

Yes, no problem. I used to do exactly that and also added a line in the config that both nodes should always attempt to connect to eachother.

Use -addnode=<ip> to add a node to connect to and attempt to keep the connection open.