There is no dedicated server as such for Stardew Valley.
Instead, the implementation in AMP uses a SMAPI (Stardew Modding API) mod that simulates a server by using a headless automated bot to act as the host player in a running instance of the game.
Since the “server” is just running the game, the port used is not configurable and so will always use the default 24642/UDP. As such a separate Stardew Valley game client (or another “server”) cannot be run on the same host system at the same time.