A much better way to solve the issue you are having is run a small local "proxy" program on your server that does nothing but accept traffic on one port and redirect it to the port on the application that will evidently not allow you to change port.
Assume the application only listens on port 3000 and your external IP is 255.99.99.99, and you want a second instance listening on port 3001.
Under this setup, you would tell application instance A to listen on 255.99.99.99:3000, tell application instance B to listen on 127.0.0.1:3000, and tell your proxy program to listen on 255.99.99.99:3001, and to redirect incoming connections from there to 127.0.0.1:3000.
Under Linux you can do this with
iptables or another program called
rinetd. I'm sure there are equivalent programs for Windows.