You can only have one server per port, but since this is LabVIEW, you can make it handle communications for all your programs.
Is this UDP based? Write a generic server that sorts the incoming packets according to source IP or some custom tag in the packet payload to further message it to the correct task via some local mechanism.
(Simplest would be to write some kind of proxy that would listen on one port and resend all packets locally to the real port of each server program. In this solution you don't need to touch the server code at all.)