The answer to this question depends on several factors, primarily which product you are using and whether the masters are serial or ethernet. There are also practical restrictions such as polling intervals to consider.
If you have a network master, that uses a socket for the listener. Each serial port also uses a socket. So the available number of sockets for use by network slaves is the total available sockets with the listeners subtracted, the number of listeners being dependent on how many serial ports the device has and how many separate network masters are configured.
The PortServer family of products (PortServer TS 1/2/4, TS 8/16, Digi One IAP) support a total of 64 available TCP sockets for the industrial automation configuration.
The Digi One IA supports a total of 32 available TCP sockets for the industrial automation configuration.
The ConnectPort TS family of products support a total of 32 available TCP sockets.
The ConnnectPort LTS family of products support 64 TCP sockets in an industrial automation configuration.
For example, a Digi One IAP with two separate network masters will use two TCP sockets for the master listeners, and two TCP sockets for the serial listeners, leaving 60 sockets available for other connections.