You can do it like this:
Start with a closed Shape. With the Direct Selection tool, select the Shape (so you see all the points as hollow squares), and then select the edges you want to connect, either by selecting the edges themselves, or the control points. Selecting a control point will also select its associated edges, so you should not select the two end points, only the edges. Shift+clicking will allow you to select multiple edges. Copy these to the clipboard.
Make a new Shape layer, but leave it open. This can even be just a single point, but you need to have a separate Shape layer.. Paste the copied edges, and use the Pen to connect the ends of the drawn path and the pasted path. Click on one point, and you should see "Pick Up Path" in the history. Click on the other, and you should see "Join Paths".
As long as the Shape has not been closed, you can continue to copy, paste, and connect from any other previously made Shapes. Note that the shapes are independent, so if you decide to move a vertex in one, the edges will no longer be shared.
I hope that all makes sense. Here you can see the results:
