I have a 1769-L32E Compact Logix processor. I am using the EtherNet port already. I want to know if I can use the serial port to connect to another device to create another EtherNet port with a different IP address?
You should be able to accomplish what you've described through a serial to EtherNet module. Rockwell had one which is now retired, but a lot of 3rd party manufacturers still make these.
However, could you elaborate on the reason as to why you'd want to go this route? You can create any IP structure with a switch & you wouldn't need to use the serial port.