Hi all, long time no see

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We have a computer here at work that we want to make two network connections to the server with. We've been running into problems with IP addresses, and Windows apparently doesn't like that they are connected to the same destination.
Is there any way to fool Windows into thinking it's just one network connection? Or perhaps get around Windows' limitations? I specialized in hardware, but I'm the closest thing the company has to a network guy.
Thanks