It may be possible if you run them in separate user accounts that you keep logged on simultaneously. The only problem I can foresee would be if uplink uses global/pc registry keys instead of account based registry keys to store settings. If that's the case each time you configured one Uplink, the other(s) would also configure themselves with the same settings.
Another possibility is to run another Uplink in a virtual machine. A virtual machine basically emulates an entirely different computer inside another computer. The VM (even though it is running on another operating system) acts entirely independently of the host computer. This would allow you to run Windows inside a VM and run Uplink on that. This would not interfere with the host computer's operating system or Uplink. It is essentially a way to split your computer up into two. The only problem is a VM takes a lot of resources to run (lots of processor and memory required) and I very much doubt you would be able to run more than 1 VM successfully, even just 1 VM may slow everything down to the point where audio starts to break-up.