No. Not to the wired port.
To connect more than one machine at once to the network in your room would require you to extend the network using a hub, switch or wireless access point. Extending the network in this way is not permitted; the ResNet has been designed to allow you to connect a single machine at a time to the port in your bedroom. You can change the connected machine as often as you like.
There is no restriction on the number of wireless connections you can make simultaneously.