Different subnets on one physical link.

I am having a bit of mental block.  Can different subnetted ip's run over the same physical segment.  I am looking at putting my computer lab on a different subnet than the rest of my organization. The physical location dictates that some of my original subnetted equipment and the new subnet equipment have to share the same physical link  to the servers and eventually, my firewall.  I am using linksys layer 2 switches with web management.  What must I be concerned with and can the additional subnet be eventually tied into a free interface on my firewall?
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