Yes, a proxy server would allow you to use another machine's bandwidth. Basically, the proxy server makes web requests on behalf of your computer, and then relays the results. However, you are then limited to the types of traffic your proxy server can handle... usually HTTP, HTTPS, and SOCKS.
How are they tracking different machines? Typically this is done by MAC address. That being the case, if you change your MAC address (using Macshift or some other utility), it should get you back up and running. If you have to register your computers on the network somehow, it will show up as another computer for your account. If no registration is necessary, you could simply script macshift to run every time you reboot, seamlessly getting around the limit..
Another option would be to fire up VMWare or some other virtualization software and build a machine with 20 virtual bridged NICs or so. Install routing software to load balance among all of them. Then, set up you and your friends to use it as a gateway on a different subnet altogether. This is probably overkill.
Your best option? Talk to your IT department. Bandwidth is limited for a reason, but if you have a reason to go over that limit, see what your options are. I'm willing to bet that they will make an exception for you, provided you aren't pirating your DVD collection.