You can do exactly that.
Here are the complications:
1. You will need a separate address range on one side of the server. 192.168.1.0 is fine.
2. You will have to modify your DHCP server to hand out correct addresses on each LAN.
3. Youwill have to enable IP routing so that the server routes between the two LANs.
4. If there is a router which is everyone's default gateway, you will have to modify the stations you are moving to make the server (the new NIC) their default gateway.
5. If the default gateway is a router, and it is doing NAT, you will have to tell it about the additional address range (to do NAT for it), and set a static route for the new range, pointing at the server (the old NIC).
6. Often, adding a second NIC works better if they are different brands. That way the drivers do not get confused over which driver is running which card.
Good luck.