How do I get multiple connections from a Subnetwork input port?

I've published a port "shape", and I need both the center point of the shape and the geometry. How do I accomplish this?

Coming in or coming out? In both cases send the shape (you have that coming in or out) to a centerpoint node. I do not see the problem. Can you explain a bit more?

The output of the subnetwork is whatever is the rendered node in the subnetwork. In your case, it makes sense to make the shape the rendered node, then use a centerpoint node to get the center point.