Replying to myself - I managed to figure it out.
The answer is yes, it is possible. To do it:
1) Click on the host ip,
2) Click on the "Configuration" Tab
3) Click the "Networking" link under the "Hardware" heading
4) On the far right, click "Add Networking..."
5) In the window that pops up, select "Virtual Machine"
6) Click next, then you will see a list of available ports (In my case 12 ethernet ports available). Pick the one you want, click next and finish!
So now when you edit "Edit Settings..." for an individual virtual machine You can "Add..." a network adapter. Fantastic.