The correct question to ask is "How many sockets can I keep open per server".
It depends on the OS.
Linux:
The value set to net.ipv4.netfilter.ip_conntrack_max
Windows:
70,000 connections on a reasonably low spec VM
Max tcp/ip connections on Windows Server 2008
Then it of course depends on how well written your application is, the hardware spec etc etc.
So I would say that you should not design your application per the amount of open sockets because your application would probably crash and burn before the socket limit is reached.