When a TCP Server does a socket accept on a port, it gets a new socket to work with that Client.
The accepting socket remains valid for that port and can accept further
The IETF has banned the practice of allocating more than one port for new protocols so we likely won't be seeing this in the future.
Newer IP protocols such as SCTP are designed to solve some of the shortcommings of TCP that could lead one to use multiple ports. TCPs 'head-of-line' blocking prevents you from having multiple separate requests/streams in flight which can be a problem for some realtime applications.