You can have multiple different protocols handled by the same port but there are some caveats:
The must be some way for the server to detect (or negotiate) the protocol that the client wishes to speak. You can think of separate ports as the normal way of detecting the protocol the client wishes to speak.
Only one server process can be actually listening on the port. This server might only serve the purpose of detecting the type of protocol and then forwarding to multiple other servers, but each port is owned by a single server process.
You can't support multiple protocols where the server speaks first (because there is no way to detect the protocol of the client). You can support a single server-first protocol with multiple client-first protocols (by adding a short delay after accept to see if the client will send data), but that's a bit wonky.
An explicit design goal of the WebSocket protocol was to allow WebSocket and HTTP protocols to share the same server port. The initial WebSocket handshake is an HTTP compatible upgrade request.
The websockify server/bridge is an example of a server that can speak 5 different protocols on the same port: HTTP, HTTPS (encrypted HTTP), WS (WebSockets), WSS (encrypted WebSockets), and Flash policy response. The server peaks at the first character of the incoming request to determine if it is TLS encrypted (HTTPS, or WSS) or whether it begins with "<" (Flash policy request). If it is a Flash policy request, then it reads the request, responds and closes the connection. Otherwise, it reads the HTTP handshake (either encrypted or not) and the Connection and Upgrade headers determine whether it is a WebSocket request or a plain HTTP request.
Disclaimer: I made websockify